Question

How do you factor `2x^2+11x+15`?

Answer 1

`(2x+5)(x+3)`

Explanation:

To factor this expression we will need to factor each of the terms individually so that when we reverse the factorization, the terms will re-multiply into the given expression.

Given: `2x^2 + 11x + 15`

Because we start out with `x^2` we know we will end up with two brackets: `( ...)( ...)`

We know that each bracket will need an `x` inside: `(x...)(x...)`

In this case we can see that one of the `x` terms will need to be multiplied by 2 since we start with `2x^2`. So `(2x...)(x...)`

We know that each bracket will need a numerical factor. In this case the number to be factored is: `15=(15)(1) =(3)(5)=(5)(3)`

So we can write in:`(2x...15)(x...1) = (2x...3)(x...5) = (2x...5)(x...3)`

But we need to have factors that when multiplied by `x` will add or subtract to result in the central term of the expression - in this case `11x`.

We can see that `2*3 = 6 and 5*1 = 5` will result in `11` when added. This indicates both numeric terms need to be `+`.

The given expression also agrees with the double `+`, because both signs are `+`.

Then we can write: `2x^2 + 11x + 15 = (2x+5)(x+3)`

To check for correctness, simply re-multiply the answer to result in the given expression.