How do you factor: y=x2+7x+12?

3 Answers
Apr 12, 2018

y=(x+4)(x+3)

Explanation:

y=x2+7x+12)

y=(x+4)(x+3)

Apr 12, 2018

(x+3)(x+4)

Explanation:

the factors of + 12 which sum to + 7 are + 3 and + 4

x2+7x+12=(x+3)(x+4)

Apr 12, 2018

(x+4)(x+3)

Explanation:

If a quadratic with 3 terms; one with a coefficient of x, for example, x2,2x2,3x2 etc, a value of x and a constant usually the factorised form includes 2 brackets.

When factorising that has 2 brackets we need 2 numbers that add up to make the second term and the same 2 numbers to multiply to get the second term.

I usually start by listing the factors of the third term which is 12:

12 and 1

As 12 and 1 cannot add or subtract to make 7 this pair does not work.

6 and 2

As 6 and 2 cannot add or subtract to make 7 this pair does not work.

4 and 3

4 and 3 add to make 7 so we can use this.

With all of the signs being positive within x2+7x+12, both 4 and 3 have to be both positive.

(x+3)(x+4)

Remember you can always expand each term to check:

(x+3)(x+4)

x×x=x2

x×4=4x

3×x=3x

3×4=12

x2+4x+3x+12

x2+7x+12

This is the same as what we started with, therefore, it is correctly factorised.

(x+4)(x+3)