Question

Factor this polynomial.
-3x^2– 5x-2

Answer 1

`-(3x+2)(x+1)`

Explanation:

So we have the polynomial:

`-3x^2-5x-2\\=-(3x^2+5x+2)`

(I moved the negative to the outside. This is optional, but it makes things cleaner and you will have to do it eventually.)

This is a quadratic. To factor this, we need to find two numbers p and q such that:

`p\cdot q=ac\\p+q=b`

From there, we can substitute these numbers in for b.

From the quadratic, a=3, b=5, and c=2. We ignore the negative sign.

In other words, ac=6 and b=5.

After guessing and checking, two numbers that work are 3 and 2 since 3(2)=6 ad 3+2=5. We substitute these values in for b. So:

`-(3x^2+5x+2)\\-(3x^2+3x+2x+2)\\=-(3x(x+1)+2(x+1))\\=-(3x+2)(x+1)`