Chapter 3 Factoring. 1. Write the prime factorization of 630. 630 2315 563 321 37 = 2 x 3 2 x 5 x 7.
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Transcript of Chapter 3 Factoring. 1. Write the prime factorization of 630. 630 2315 563 321 37 = 2 x 3 2 x 5 x 7.
Chapter 3
Factoring
1. Write the prime factorization of 630.
630
2 315
5 63
3 21
3 7
= 2 x 32 x 5 x 7
56
881, 56 2, 28, 4, 14, 7, 8,
1, 88 2, 44, 4, 22, 8, 11,
2. Determine the greatest common factor of 56 and 88.
56
2 28
2 14
2 7
GCF = 2x2x2
2. Determine the greatest common factor of 56 and 88.
88
2 44
2 22
2 11
= 8
10
2210, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110,
22, 44, 66, 88, 110, 132, 154, 176, 198, 220, 240
3. Determine the least common multiple of 10 and 22.
120,
3. Determine the least common multiple of 10 and 22.
LCM = 2x5x11
10
2 5
22
2 11
LCM = 110
Circle prime factors so the highest power of each prime is selected, then multiply those to
find LCM
= 2 x 5 = 2 x 11
4. Determine the edge length of this cube.
Volume3= 91 125 cm
V = (x)(x)(x)
hwV
91125 = x3
x3 91125
x = 45 cm
5. Factor the binomial 29944 aa
= 11a(4
6. Factor the trinomial 3223 324024 cddcdc
= -8cd(
3c2+ 5cd+ 4d2)
+ 9a)
7. Expand and simplify: 235 nm
= 25m2
– 15mn )35(35 nmnm – 15mn + 9n2
= 25m2
8. Expand and simplify:
= 56h3– 32h2
)147(38 2 hhh
+21h2
= 56h3
+ 8h – 12h +3
– 30mn + 9n2
– 11h2 – 4h +3
9. Expand and simplify:
= 10x4– 4x3
)325(652 22 xxxx
+ 6x2+ 25x3 – 10x2 + 15x– 30x2 – 18
– 34x2
+ 12x
= 10x4+21x3 + 27x
– 18
10. Expand and simplify:
= (18x2
+ 48xy
yxyxyxyx 3232836
– 3xy
– 8y2) 4x2 – 6xy +9y2)
= 14x2
– 6xy
= (18x2 + 45xy – 8y2)
– (4x2 – 12xy +9y2)
+ 57xy – 17y2
232836 yxyxyx
– (
11. Factor the following:
a) 1242 xx
= (x )(x )+ 6 – 2
No
-12
+6 & -2
Is there a common factor?Step 1
Multiply (+1)(-12)
2
Look for numbers: ___ x ___ -12 ___ + ___ +4
3
4 Split into Brackets. First coefficient is always the same as original expression.Divide by the GCF in each bracket
5
11. Factor the following:
b) 4129 2 cc
= (9c )(9c )– 6 – 6
No+36
-6 & -63 3
= (3c– 2)(3c– 2)
Is there a common factor?Step 1
Multiply (+9)(+4)
2
Look for numbers: ___ x ___ +36 ___ + ___ -12
3
4 Split into Brackets. First coefficient is always the same as original expression.Divide by the GCF in each bracket
5
= (3c– 2)2
11. Factor the following:
c)
= 2(12b )(12b )+ 28 – 3
-84
+28 & -3
4 3
=2(3b + 7)(4b – 1)
Is there a common factor?Step 1
Multiply (+12)(-7)
2
Look for numbers: ___ x ___ -84 ___ + ___ +25
3
4 Split into Brackets. First coefficient is always the same as original expression.Divide by the GCF in each bracket
5
145024 2 bb
Yes
= 2( 12b2 + 25b – 7)
11. Factor the following:
d)= (7s 8t)(7s 8t)+ –
Is there a common factor?Step 1
Take the square root of both terms and separate into two sets of brackets.
2
One Positive and One Negative
3
No
22 6449 ts
Difference of Squares
11. Factor the following:
e)
= (8c d)(8c d)+ 20 – 2
-40
+20 & -2
4 2
=(2c + 5d)(4c – d)
Is there a common factor?Step 1
Multiply (+8)(-5)2
Look for numbers: ___ x ___ -40 ___ + ___ +18
3
4 Split into Brackets. First coefficient is always the same as original expression.Divide by the GCF in each bracket
5
No22 5188 dcdc
11. Factor the following:
f)
Is there a common factor?Step 1
Take the square root of both terms and separate into two sets of brackets.
2
One Positive and One Negative
3
YesDifference of
Squares24 7683 zz
= 3z2( – 256)z2
= 3z2(z 16)(z 16)+ –
12. Calculate the area of the shaded regionLarge Rectangle:
Small Rectangle:
1332 xx
= 6x2– 2x + 9x
= 6x2 + 7x – 3
– 3
12 xx
= 2x2– x
AShaded = (6x2 + 7x – 3)
– (2x2 – x)
= 4x2+ 8x– 3
Algebra Tiles
+x2 -x2
+x+x-x
-x
+1
-1
13. Draw the following factors using algebra tiles. There is a legend on your formula sheet:
a)652 xx
Step 1: Factor
= (x + 3)(x + 2)
+6 This is the number of small tiles
This is the number of big tiles
Represents the long skinny tiles(x +
3)
(x +
2
)
13. Draw the following factors using algebra tiles. There is a legend on your formula sheet:
b)232 xx
Step 1: Factor
= (x – 2)(x – 1)
+2This is the number of small tiles
This is the number of big tiles
Represents the long skinny tiles
(x – 2)
(x –
1)
13. Draw the following factors using algebra tiles. There is a legend on your formula sheet:
c)62 2 xx
Step 1: Factor
= (x + 2)(2x – 3)
-12This is the number of small tiles
This is the number of big tiles
Represents the long skinny tiles
(2x – 3)
(x +
2
)
__ x __ = -12__+__ = +1
= (2x + 4)(2x – 3)2 1
13. Draw the following factors using algebra tiles. There is a legend on your formula sheet:
d)322 xx
Step 1: Factor
-3This is the number of small tiles
This is the number of big tiles
Represents the long skinny tiles
(x – 3)
(x +
1
)__ x __ = -3__+__ = -2
= (x + 1)(x – 3)