Factoring Trinomials 9-4

ax2 + bx +c Chapter 9

Check to see if there are any common factors.

2x2 + 22x + 362 is a common

factor

2x2 + 22x + 36

Factor out a 2

2(x2 + 11x + 18)Hint: Divide each number by 2

2(x2 + 11x + 18)Now factor

(x2 + 11x + 18)

Hint: Look at the signs. Will you be adding or subtracting?

(x2 + 11x + 18)

(x + )(x + )

Hint: Start by finding the factors of x.

(x2 + 11x + 18) (x + )(x + )

Find the factors of 18 that will add to get

11.

(x2 + 11x + 18)

The factors of 18 are

1,2,3,6,9,18

2 and 9 add to be 11

(x2 + 11x + 18)(x + 2)(x + 9)

Is the answer for

(x2 + 11x + 18)

The final answer is

Now put it all together

2(x + 2)(x + 9)Add the 2 we

factored out to the answer.

Prime Polynomial

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

Example8b2 -5b -10 multiply the a and c8 * -10 = -80

Factors of -80 would be

1, -80 8, -10

2, -40

4, -20 No factors have a sum of -5

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

7x2 + 22x +3

21 Sum

1, 21 22 so m = 1 and n = 21

Now put these factors into the pattern ax2 + mx + nx + c

7x2 + x + 21x + 3

7x2 + x + 21x + 3

Group terms with common factors

(7x2 + x) + (21x + 3)

x(7x + 1) + 3(7x + 1)

(x + 3)(7x + 1) the answer