Question

Please Factor -5x²+13x+6

Answer 1

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

or
`-(x-3)(5x+2)`

Explanation:

quadratic equation format:
`a^2+b^2+c`

Therefore, for
`-5x^2+13x+6`, a = -5, b = 13 and c = 6

Multiply the coefficient of
`x^2` (
`a`) by the constant term (
`c`)

`\implies -5 * 6 = -30`

Find two numbers which have a product of -30 and a sum of
`b` (13)

Factors of 30: 1 and 30, 2 and 15, 3 and 10, 5 and 6

So -2 and 15 have a product of -30 and sum of 13.

Rewrite
`13x` as
`15x-2x` and substitute into the equation:

`\implies -5x^2+15x-2x+6`

Factorize the first two terms and the last two terms separately:

`\implies-5x(x-3)-2(x-3)`

The bracket created should always be the same.

The two brackets have now been found. The first bracket is the common factor of (x - 3). The second bracket is the factorized terms outside of each bracket (-5x - 2).

`\implies (x-3)(-5x-2)`

Additionally, we can write (-5x - 2) as -(5x + 2)

`\implies -(x-3)(5x+2)`