Question

What is the factorization of the polynomial below?
5x2 - 35x + 60

Answer 1

`5(x-3)(x-4)`

Explanation:

`5x^2-35x+60`

Start by factoring out a 5:

`5(x^2-7x+12)`

We need to find two integers that have a product of 12, and a sum of -7:

(-3)(-4)=12

-3-4=-7

We can split -7x into -3x and -4x

`5(x^2-3x-4x+12)`

Factor each half separately:

`5[x(x-3)-4(x-3)]`

Since x and -4 are both being multiplied by x-3, we can combine them:

`5(x-3)(x-4)`