Question

Factorise fully the following:

a) x² + 2x
b) 2x² - 6x
c) 15x - 10x³
d) 9x² + 3x³​

Answer 1

a)
`x(x+2)`

b)
`2x(x-3)`

c)
`5x(3-2x^2)`

d)
`3x^2(3+x)`

Explanation:

a)
`x^2+2x`

When factoring a binomial (a polynomial with two terms), what we will be looking for are the terms that are shared between them.

In this problem, it can be seen that both of these terms have and x. This means that we can factor it out to get

`x(x+2)`

b)
`2x^2-6x`

What are the common terms here?

It can be seen that each of these share a 2x, so our factored form would be

`2x(x-3)`

c)
`15x-10x^3`

What about this one?

The common factor of this one is 5x, so our factored form would be

`5x(3-2x^2)`

d)
`9x^2+3x^3`

The common factor of this one is
`3x^2`, so our factored form would be

`3x^2(3+x)`