Factoring Quadratic Trinomial

​Factoring: Quadratic Trinomial when a=1

​A quadratic trinomial is an algebraic expression​ with 3 terms separated by + and - with a degree of 2. The largest power of x is 2.

What is a quadratic trinomial?​

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• List all of the factors of c

• Decide which combination of numbers will add up to b ( keep their signs)

• Write the factored form: (x+__)(x+__)

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​Some text here about the topic of discussion.

Factoring trinomials of the form

ax²+bx+c​

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Multiple Choice

In order to factor the trinomial,  ax²+bx+c  we need to find two integers that....?

• the sum is equal to c

• the sum is equal to b

• the difference is equal to a

• the difference is equal to b

​Factoring when b and c are positive

​If b and c are both positive, the factors are of the forms (x+_) (x+_) and the two numbers that we are looking for are both positive.

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Multiple Choice

Factor:

b² + 8b + 7

• (b + 4)(b + 3)

• (b + 6)(b + 1)

• (b+9)(b-1)

• (b + 7)(b +1)

​Factoring when b is negative & c is positive

​If b is negative and c is positive, it tells us that the two numbers that we are looking for are both negative.

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Example: x² - 7x + 12 = (x-3)(x-4)​

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Multiple Choice

Factor x²-7x+10

• (x-5) (x-2)

• (x-5) (x+2)

• (x+5) (x-2)

• (x+5) (x+2)

​Factoring when c is negative

​When c is negative, it means ​that the two numbers have a different sign. The sign of the middle term tells you the sign of the larger number.

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Examples: x² + 11x - 12 = (x+12)(x-1)

x² - 7x - 18 = (x -9)(x+2)

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Multiple Choice

Factor

x² + 9x - 36

• (x + 12)(x - 3)

• (x + 9)(x - 4)

• (x - 9)(x - 4)

• (x - 12)(x + 3)

Multiple Choice

Factor

m² - m - 12

• (a + 4)(a - 3)

• (a + 6)(a - 2)

• (a - 4)(a + 3)

• (a - 6)(a + 2)