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

Chapter 9

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**Check to see if there are any common factors.**

2x2 + 22x + 36 2 is a common factor

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**2x2 + 22x + 36 Factor out a 2 2(x2 + 11x + 18)**

Hint: Divide each number by 2

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**2(x2 + 11x + 18) (x2 + 11x + 18) Now factor**

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

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

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**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.

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**(x2 + 11x + 18) The factors of 18 are 1,2,3,6,9,18**

2 and 9 add to be 11

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

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**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.

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

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**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

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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

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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

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**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

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