Question

Factorise 3x^2+9x-12 please help.

Answer 1

`3(x-1)(x+4)`

Explanation:

1) Find the Greatest Common Factor (GCF).

1 - What is the largest number that divides evenly into
`3x^2,9x,` and
`-12`?

It is 3.

2 - What is the highest degree of
`x` that divides evenly into
`3x^2,9x,` and
`-12`?

It is 1, since x is not in every term.

3 - Multiplying the results above,

The GCF is 3.

2) Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

`3((3x^2)/(3) +(9x)/(3) -(12)/(3) )`

3) Simplify each term in parentheses.

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

4) Factor
`x^2+3x-4`.

1 - Ask: Which two numbers add up to 3 and multiply to -4?

- 1 and 4

2 - Rewrite the expression using the above.

`(x-1)(x+4)`

Answer:

`3(x-1)(x+4)`