Factor completely: 2x +11x +12?

1 Answer
Apr 13, 2018

(2x+3)(x+4)

Explanation:

If you mean:

2x+11x+12

This simplifies to:

13x+12

Which factors to:

-> 1(13x+12) as nothing is common between the two terms apart from 1 of course...

If you mean 2x^2+11x+12

Multiply the coefficient by the constant:

2 xx 12=24

We are trying to find a pair of numbers that add to make 11 and multiply to make 24. Start out by listing the factors of 24

24 and 1
12 and 2
8 and 3
6 and 4

By looking at these pairs we can conclude that 8+3 makes 11, so we use these.

As all terms are positive, all numbers have to be positive

Plugging back in:

2x^2+8x+3x+12

Notice that we use the original +12, we only multiply to find the values to factor

Factor the two first terms:

2x^2+8x -> 2x(x+4)

Factor out the last two terms:

3x+12 -> 3(x+4)

therefore 2x^2+8x+3x+12 -> 2x(x+4)+3(x+4) <- Notice these brackets are the same

One bracket is (x+4), the other is the remaining terms which is (2x+3)

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

We can always expand to check:

2x xx x=2x^2

x xx 3 =3x

4 xx 2x=8x

4 xx 3=12

-> 2x^2+8x+3x+12 -> 2x^2+11x+12

Therefore this is factorised correctly.