Factoring Trinomials 9-4 ax2 + bx +c

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

Check to see if there are any common factors. 2x2 + 22x + 36 2 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) (x2 + 11x + 18) Now factor Hint: Look at the signs. Will you be adding or subtracting?

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

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.

(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)

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.

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

Example 8b2 -5b -10 multiply the a and c 8 * -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 (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