Question

Factor the polynomial: x2+7x+12 A (x + 3)(x + 4) B (x + 2)(x + 6) C (x + 1)(x + 12) D (x + 7)(x + 12)

Answer 1

a: (x + 3)(x + 4)

Explanation:

assuming x^2 + 7x + 12 is the equation you are factoring

you would first multiply a * c

a is 1

b is 7

c is 12

1 * 12 = 12

then you take b and find what adds up to b but multiplies to ac

what adds up to 7 but multiplies to 12

3 and 4

so

you split the equation up like this

x^2 + 3x + 4x + 12

then you factor

x(x + 3) + 4(x + 3)

because x + 3 and x + 3 are the same we can do this

(x + 4)(x + 3)

that is your equation

so a is your answer

it doesnt matter if you have the (x + 3) or (x + 4) in the front

Answer 2

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Answer:
`\textsf{Option A, (x + 3)(x + 4)}`

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In order to factor the polynomial we need to first split the middle term so it add up to 7 but multiplies to 12. We know that 3 and 4 can do that. We would the factor by grouping which would give us our final answer.

`x^2 + 7x + 12`

`x^2 + 4x + 3x + 12`

`x(x + 4) + 3(x + 4)`

`(x + 3)(x + 4)`

Answer:
`\textsf{Option A, (x + 3)(x + 4)}`