Question

How do you factor `5x^3+6x^2-45x-54`?

Answer 1

(5x +6)(x-3)(x+3)

Explanation:

Group the terms in 'pairs'

thus `[5x^3+6x^2]+[-45x-54]`

now factorise each pair

`rArrx^2(5x+6)-9(5x+6)`

We now have a common factor of (5x + 6) and taking it out leaves.

`(5x+6)(x^2-9)`

Now `x^2-9" is a difference of squares"`

In general a difference of squares factorises as.

`color(red)(|bar(ul(color(white)(a/a)color(black)(a^2-b^2=(a-b)(a+b))color(white)(a/a)|)))`

here `x^2=(x)^2" and " 9=(3)^2rArra=x ,b=3`

`rArrx^2-9=(x-3)(x+3)`

Putting this altogether to obtain.

`5x^3+6x^2-45x-54=(5x+6)(x-3)(x+3)`