Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a...
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![Page 1: Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a monomial, divide each term in the polynomial by the.](https://reader038.fdocuments.us/reader038/viewer/2022103100/56649ef45503460f94c06a90/html5/thumbnails/1.jpg)
Dividing Polynomials &
The Remainder Theorem
![Page 2: Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a monomial, divide each term in the polynomial by the.](https://reader038.fdocuments.us/reader038/viewer/2022103100/56649ef45503460f94c06a90/html5/thumbnails/2.jpg)
Dividing Polynomials
• When dividing a polynomial by a monomial, divide each term in the polynomial by the monomial
• Ex.
xy
yxxyyx
4
1284 32223
![Page 3: Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a monomial, divide each term in the polynomial by the.](https://reader038.fdocuments.us/reader038/viewer/2022103100/56649ef45503460f94c06a90/html5/thumbnails/3.jpg)
Dividing Polynomials
• When dividing a polynomial by a polynomial, use long division (called division algorithm)
• Ex.
122 5934242 tttxxx
![Page 4: Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a monomial, divide each term in the polynomial by the.](https://reader038.fdocuments.us/reader038/viewer/2022103100/56649ef45503460f94c06a90/html5/thumbnails/4.jpg)
More Dividing
2
810135235
2312
x
xxxaaa
![Page 5: Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a monomial, divide each term in the polynomial by the.](https://reader038.fdocuments.us/reader038/viewer/2022103100/56649ef45503460f94c06a90/html5/thumbnails/5.jpg)
Dividing
113124254 524 mmmyyyy
![Page 6: Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a monomial, divide each term in the polynomial by the.](https://reader038.fdocuments.us/reader038/viewer/2022103100/56649ef45503460f94c06a90/html5/thumbnails/6.jpg)
Dividing, one more
2628156 34 xxxx
![Page 7: Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a monomial, divide each term in the polynomial by the.](https://reader038.fdocuments.us/reader038/viewer/2022103100/56649ef45503460f94c06a90/html5/thumbnails/7.jpg)
Synthetic Division—shortcut to long division—only use if dividing by
--where a is a constant ax
_____________________
8101352
2810135 23
xxxx
![Page 8: Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a monomial, divide each term in the polynomial by the.](https://reader038.fdocuments.us/reader038/viewer/2022103100/56649ef45503460f94c06a90/html5/thumbnails/8.jpg)
More synthetic Division
• Remember if you are missing a term, you need to put in a zero for the coefficient
12
25
593
2883
ttt
zzz
![Page 9: Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a monomial, divide each term in the polynomial by the.](https://reader038.fdocuments.us/reader038/viewer/2022103100/56649ef45503460f94c06a90/html5/thumbnails/9.jpg)
More synthetic Division
32314174 24 xxxx
![Page 10: Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a monomial, divide each term in the polynomial by the.](https://reader038.fdocuments.us/reader038/viewer/2022103100/56649ef45503460f94c06a90/html5/thumbnails/10.jpg)
The Remainder Theorem
If you divide a polynomial of degree by then the remainder is
![Page 11: Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a monomial, divide each term in the polynomial by the.](https://reader038.fdocuments.us/reader038/viewer/2022103100/56649ef45503460f94c06a90/html5/thumbnails/11.jpg)
Example
Given , find
![Page 12: Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a monomial, divide each term in the polynomial by the.](https://reader038.fdocuments.us/reader038/viewer/2022103100/56649ef45503460f94c06a90/html5/thumbnails/12.jpg)
Example
Given , find
![Page 13: Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a monomial, divide each term in the polynomial by the.](https://reader038.fdocuments.us/reader038/viewer/2022103100/56649ef45503460f94c06a90/html5/thumbnails/13.jpg)
Example
Given , find
![Page 14: Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a monomial, divide each term in the polynomial by the.](https://reader038.fdocuments.us/reader038/viewer/2022103100/56649ef45503460f94c06a90/html5/thumbnails/14.jpg)
The Factor Theorem
Let be a polynomial.
a. If then is a factor of
b. If is a factor of then
![Page 15: Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a monomial, divide each term in the polynomial by the.](https://reader038.fdocuments.us/reader038/viewer/2022103100/56649ef45503460f94c06a90/html5/thumbnails/15.jpg)
Is a factor of
If it is, write as a product of two factors.
![Page 16: Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a monomial, divide each term in the polynomial by the.](https://reader038.fdocuments.us/reader038/viewer/2022103100/56649ef45503460f94c06a90/html5/thumbnails/16.jpg)
Use the Factor Theorem to Solve
Solve the equation given that 3 is a zero of the function.
![Page 17: Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a monomial, divide each term in the polynomial by the.](https://reader038.fdocuments.us/reader038/viewer/2022103100/56649ef45503460f94c06a90/html5/thumbnails/17.jpg)
Solve
given that -1 is a zero of the function.