Other types of Equations Polynomial Equations. Factoring Solve.
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Transcript of Other types of Equations Polynomial Equations. Factoring Solve.
![Page 1: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/1.jpg)
Other types of Equations
Polynomial Equations
![Page 2: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/2.jpg)
Factoring
• Solve 24 483 xx
![Page 3: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/3.jpg)
Factoring
• Solve
• First, set the equation equal to zero.
24 483 xx
0483 24 xx
![Page 4: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/4.jpg)
Factoring
• Solve
• First, set the equation equal to zero.
• Take out the common factor.
24 483 xx
0483 24 xx
0)16(3 22 xx
![Page 5: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/5.jpg)
Factoring
• Solve
• First, set the equation equal to zero.
• Take out the common factor. Factor.
24 483 xx
0483 24 xx
0)16(3 22 xx 0)4)(4(3 2 xxx
![Page 6: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/6.jpg)
Factoring
• Solve
• First, set the equation equal to zero.
• Take out the common factor. Factor. Solve.
24 483 xx
0483 24 xx
0)16(3 22 xx 0)4)(4(3 2 xxx
0
03 2
x
x4
04
x
x
4
04
x
x
![Page 7: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/7.jpg)
Factoring
• You try: xx 82 3
![Page 8: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/8.jpg)
Factoring
• You try: xx 82 3
)2)(2(2
0)4(2
0822
3
xxx
xx
xx
![Page 9: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/9.jpg)
Factoring
• You try: xx 82 3
)2)(2(2
0)4(2
0822
3
xxx
xx
xx
0
02
x
x
2
02
x
x
2
02
x
x
![Page 10: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/10.jpg)
Factor by grouping
• When you have a 3rd degree equation with four terms, you will factor by grouping.
0933 23 xxx
![Page 11: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/11.jpg)
Factor by grouping
• When you have a 3rd degree equation with four terms, you will factor by grouping.
0933 23 xxx
0)3(3)3(2 xxx
![Page 12: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/12.jpg)
Factor by grouping
• When you have a 3rd degree equation with four terms, you will factor by grouping.
0933 23 xxx
0)3(3)3(2 xxx
0)3)(3( 2 xx
3
03
x
x
3
3
032
2
ix
x
x
![Page 13: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/13.jpg)
Factor by grouping
• You try: 0632 23 xxx
![Page 14: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/14.jpg)
Factor by grouping
• You try: 0632 23 xxx
0)3)(2(
0)2(3)2(2
2
xx
xxx
![Page 15: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/15.jpg)
Factor by grouping
• You try: 0632 23 xxx
0)3)(2(
0)2(3)2(2
2
xx
xxx
2
02
x
x
3
3
032
2
ix
x
x
![Page 16: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/16.jpg)
Solving a 4th degree
• We will look at a 4th degree equation just like we did a 2nd degree equation. Now, instead of starting your factoring with an , it will be an .2xx
![Page 17: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/17.jpg)
Solving a 4th degree
• We will look at a 4th degree equation just like we did a 2nd degree equation. Now instead of starting your factoring with an , it will be an .
• Solve
2xx
023 24 xx
![Page 18: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/18.jpg)
Solving a 4th degree
• We will look at a 4th degree equation just like we did a 2nd degree equation. Now instead of starting your factoring with an , it will be an .
• Solve
2xx
023 24 xx
0_)_)(( 22 xx
0)1)(2( 22 xx
![Page 19: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/19.jpg)
Solving a 4th degree
• We will look at a 4th degree equation just like we did a 2nd degree equation. Now instead of starting your factoring with an , it will be an .
• Solve
2xx
023 24 xx
0_)_)(( 22 xx
0)1)(2( 22 xx
0)1)(1)(2( 2 xxx
![Page 20: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/20.jpg)
Solving a 4th degree
• We will look at a 4th degree equation just like we did a 2nd degree equation. Now instead of starting your factoring with an , it will be an .
• Solve
2xx
023 24 xx
0_)_)(( 22 xx
0)1)(2( 22 xx
0)1)(1)(2( 2 xxx
2
2
022
2
x
x
x
1,01
1,01
xx
xx
![Page 21: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/21.jpg)
Solving a 4th degree
• You try: 0365 24 xx
![Page 22: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/22.jpg)
Solving a 4th degree
• You try: 0365 24 xx
0)4)(9( 22 xx
![Page 23: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/23.jpg)
Solving a 4th degree
• You try: 0365 24 xx
0)4)(3)(3(
0)4)(9(2
22
xxx
xx
![Page 24: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/24.jpg)
Solving a 4th degree
• You try: 0365 24 xx
0)4)(3)(3(
0)4)(9(2
22
xxx
xx
3
03
x
x
3
03
x
x
ix
x
x
2
4
042
2
![Page 25: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/25.jpg)
Equations involving radicals
• Solve: 272 xx
![Page 26: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/26.jpg)
Equations involving radicals
• Solve:
• First, get the radical by itself.
272 xx
272 xx
![Page 27: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/27.jpg)
Equations involving radicals
• Solve:
• First, get the radical by itself.
• Next, square both sides.
272 xx
272 xx
4472 2 xxx
![Page 28: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/28.jpg)
Equations involving radicals
• Solve:
• First, get the radical by itself.
• Next, square both sides.
• Solve.
272 xx
272 xx
4472 2 xxx
0322 xx
![Page 29: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/29.jpg)
Equations involving radicals
• Solve:
• First, get the radical by itself.
• Next, square both sides.
• Solve.
272 xx
272 xx
4472 2 xxx
0322 xx )1)(3(0 xx 1
3
x
x
![Page 30: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/30.jpg)
Equations involving radicals
• Solve:
• Now, you have to be careful. By squaring both sides, you may introduce an extraneous solution. You must check each solution.
272 xx
![Page 31: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/31.jpg)
Equations involving radicals
• Solve:
• Now, you have to be careful. By squaring both sides, you may introduce an extraneous solution. You must check each solution.
272 xx
1
3
x
x
231
2)3(7)3(2
213
2)1(7)1(2
![Page 32: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/32.jpg)
Equations involving radicals
• Solve:
• The only solution to this equation is .
272 xx
1x
![Page 33: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/33.jpg)
Equations involving radicals
• You try: 33 xx
![Page 34: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/34.jpg)
Equations involving radicals
• You try: 33 xx
1,6
)1)(6(0
670
963
)3()3(
2
2
22
x
xx
xx
xxx
xx
![Page 35: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/35.jpg)
Equations involving radicals
• You try:
• You need to check each answers.
33 xx
1,6
)1)(6(0
670
963
)3()3(
2
2
22
x
xx
xx
xxx
xx
3141
3636
![Page 36: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/36.jpg)
Equations involving radicals
• You try:
• You need to check each answers. The only answer is x = 6.
33 xx
1,6
)1)(6(0
670
963
)3()3(
2
2
22
x
xx
xx
xxx
xx
3141
3636
![Page 37: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/37.jpg)
Equations involving radicals
• You try: 035 x
![Page 38: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/38.jpg)
Equations involving radicals
• You try: 035 x
35 x
4
95
x
x
![Page 39: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/39.jpg)
Equations involving radicals
• You try:
• Check your answer.• The answer works.
035 x
35 x
4
95
x
x
03)4(5
![Page 40: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/40.jpg)
Absolute Value
• Absolute value represents distance from zero, that is why it is always positive. There will be two answers since we can go to the right from zero or to the left. 3 and -3 are both the same distance from zero.
![Page 41: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/41.jpg)
Absolute Value
• Solve: 3|| x
![Page 42: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/42.jpg)
Absolute Value
• Solve:
• The answer is , since they are both 3 units from zero.
3|| x
3
![Page 43: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/43.jpg)
Absolute Value
• Solve: 4|7| x
![Page 44: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/44.jpg)
Absolute Value
• Solve:
• We want to be 4 units from zero. There are two solutions.
4|7| x
7x
![Page 45: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/45.jpg)
Absolute Value
• Solve:
• We want to be 4 units from zero. There are two solutions.
4|7| x
7x
3
47
x
x
11
47
x
x
![Page 46: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/46.jpg)
Absolute Value
• You try: 9|52| x
![Page 47: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/47.jpg)
Absolute Value
• You try: 9|52| x
7
142
952
x
x
x
2
42
952
x
x
x
![Page 48: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/48.jpg)
Absolute Value
• Solve: 64|3| 2 xxx
![Page 49: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/49.jpg)
Absolute Value
• Solve:
• We need to solve two equations.
64|3| 2 xxx
6432 xxx )64(32 xxx
![Page 50: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/50.jpg)
Absolute Value
• Solve:
• We need to solve two equations.
64|3| 2 xxx
2,3
0)2)(3(
06
6432
2
xx
xx
xx
xxx
1,6
0)1)(6(
067
6432
2
xx
xx
xx
xxx
![Page 51: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/51.jpg)
Absolute Value
• Solve:
• We need to solve two equations.
• We need to now check our answers.
64|3| 2 xxx
2,3
0)2)(3(
06
6432
2
xx
xx
xx
xxx
1,6
0)1)(6(
067
6432
2
xx
xx
xx
xxx
![Page 52: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/52.jpg)
Absolute Value
• Solve:
• We need to solve two equations.
• We need to now check our answers.• Only -3 and 1 will work.
64|3| 2 xxx
2,3
0)2)(3(
06
6432
2
xx
xx
xx
xxx
1,6
0)1)(6(
067
6432
2
xx
xx
xx
xxx
![Page 53: Other types of Equations Polynomial Equations. Factoring Solve.](https://reader035.fdocuments.us/reader035/viewer/2022081504/56649da05503460f94a8b105/html5/thumbnails/53.jpg)
Homework
• Pages 140-141• 1-13 odd• 29,31,65,66