1. Factoring Trinomials 9-4 ax2 + bx +c
Chapter 9

2. Check to see if there are any common factors.
2x2 + 22x + 36
2 is a common factor

3. 2x2 + 22x + 36 Factor out a 2 2(x2 + 11x + 18)
Hint: Divide each number by 2

4. 2(x2 + 11x + 18) (x2 + 11x + 18) Now factor
Hint: Look at the signs. Will you be adding or subtracting?

5. (x2 + 11x + 18)
(x + )(x + )
Hint: Start by finding the factors of x.

6. Find the factors of 18 that will add to get 11.
(x2 + 11x + 18)
(x + )(x + )
Find the factors of 18 that will add to get 11.

7. (x2 + 11x + 18) The factors of 18 are 1,2,3,6,9,18
2 and 9 add to be 11

8. (x2 + 11x + 18)
(x + 2)(x + 9)
Is the answer for
(x2 + 11x + 18)

9. Add the 2 we factored out to the answer.
The final answer is
Now put it all together
2(x + 2)(x + 9)
Add the 2 we factored out to the answer.

10. Prime Polynomial
A polynomial that can not be written as a product of two polynomials with integral coefficients.

11. Example 8b2 -5b -10 multiply the a and c 8 * -10 = -80
Factors of -80 would be
1, , -10
2, -40
4, No factors have a sum of -5

12. 7x2 + 22x +3
a = 7, b = 22, c = 3
We need to find two numbers whose sum = 22 and whose product = 7 * 3 = 21.
Make a list of the factors of 21

13. 7x2 + 22x +3
Sum
1, so m = 1 and n = 21
Now put these factors into the pattern ax2 + mx + nx + c
7x2 + x + 21x + 3

14. 7x2 + x + 21x + 3 (7x2 + x) + (21x + 3) x(7x + 1) + 3(7x + 1)
Group terms with common factors
(7x2 + x) + (21x + 3)
x(7x + 1) + 3(7x + 1)
(x + 3)(7x + 1) the answer