Question

Factor each trinomial. Then match the polynomial (term) on the left with its factored form (definition) on the right. 1. x2 − 7x − 12 2. x2 − x − 12 3. x2 − 4x − 12 4. x2 + 4x − 12 a. (x - 6)(x + 2) b. (x - 2)(x + 6) c. (x - 4)(x + 3) d. Prime

Answer 1

1. ---> d. Prime

2.---> c. (x-4)(x+3)

3.---> a. (x-6)(x+2)

4. ---> b. (x-2)(x+6)

Explanation:

Trinomials are three term algebraic expressions typically featuring variables to exponent powers. To break these trinomials down we factor them using the diamond method or GCF. The diamond method states that for a trinomial
`ax^2+bx+c` multiply a*c then find two numbers which multiply to this number and add to b. When you find those numbers, write them as
`(x-/+ number)(x-/+number)`.

1.
`x^2-7x-12`

a=1, c=-12

ac=-12 and add to b=-7

Not possible. PRIME. This is not possible because the factors of -12 would have two different signs and would not be able to add to -7.

2.
`x^2-x-12`

a=1, c=-12

ac=-12 and add to b=-1

Factors: C
`(x-4)(x+3)`

3.
`x^2-4x-12`

a=1, c=-12

ac=-12 and add to b=-4

Factors: A
`(x-6)(x+2)`

4.
`x^2+4x-12`

a=1, c=-12

ac=-12 and add to b=4

Factors: B
`(x-2)(x+6)`