The Remainder Theorem

A-APR 2

Explain how to solve a polynomial by factoring

One zero of f(x)=x3+x2-16x-16 is 4, what is another zero?

How did you find it?

How do you know it’s a zero?

Synthetic Division

3 22 6 19 16 4x x x x

2 6 19 16 4

26 7 2x x

Divide polynomials without messing with the variables by usingthe coefficients and constants.

Use the oppositeof the constant from the divisor.

________________________________

The first coefficient from the dividend is the first coefficient in your answer.

6Then you multiply the number in the box to the last number written under the answer line. The answer goes under the next coefficient in line.

12

Then add!!

-7

Repeat the process!!!

-14

2

4

0

The answer is--

Synthetic Division

3 2(3 8 5 7) ( 2)x x x x

3 2( ) 3 8 5 7f x x x x Given:

Use direct substitution to find: (2)f

Use synthetic division

3 2Given: 3 8 5 7

find: 3

f x x x x

f

What can you conclude if the remainder is zero? Zero of the function

Solution of the equationx-intercept

Find the factors of the polynomial provided the number given is a

solution.

3 22 3 8 3 ; 3f x x x x

Find the zeros of the polynomial provided the number given is a

solution.

3 23 15 125 ; 5g x x x x

One zero of f(x)=x3+x2-16x-16 is 4, what is another zero?

How did you find it?

How do you know it’s a zero?

Homework

P. 355 (17-22, 25, 28, 29, 36)