Question

Factor the following polynomials. (1 point each)
9. 3x2 – 12
10. 5x3y + 35x2y + 45xy

Answer 1

I'm assuming that 1 point each is supposed to be your points, so I don't want to steal them from you.

When factoring a polynomial you want to get two factors like (x+a)(x+b) where a, b are integers. It doesn't always work out well but these problems are designed so that they do factor nicely.

So let's look at the first one:

3x^2 - 12

A polynomial like this (second degree, meaning highest exponent is 2) should look like:

Ax^2 + Bx + C

where A, B, C are all integers and may or may not be negative.

In this example, we can divide the expression by 3 because 12/3 is easy and 3/3 is even easier. This gives:

3(x^2 - 4).

Here's a neat little trick:

(x + a)(x - a) = x^2 + a^2

Applying that here:

3(x^2 + 4) = 3(x^2 + 2^2)

= 3(x + 2)(x - 2).

And we're done!

Now you do the second one.

Answer 2

Oops I meant (x + a)(x - a) = x^2 - a^2

Answer 3

Thank You sooooo much