Question

How do you factor 12y^2-6y-90

Answer 1

6(y - 3)(2y + 5)

Explanation:

12y^2 - 6y - 90

Factorize

6(2y^2 - y - 15)

Split the term

6(2y^2 - 6y + 5y - 15)

Regroup terms

6((2y^2 - 6y) + (5y - 15))

Factorize

6((2y(y - 3) + 5( y - 3))

Factorize

6(y - 3)(2y + 5)

Answer 2

`6(y-3)(2y+5)`

Explanation:

`12y^2-6y-90`

First, factor out the common term of 6:

`\implies 6(2y^2-y-15)`

To factor
`(2y^2-y-15)`:

Multiply the coefficient of
`y^2` by the constant:

`\implies 2 * -15 = -30`

Now find factors of -30 that sum to the coefficient of
`-y`, i.e. -1

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

So factors of -30 that sum of -1 are: -6 and 5

Rewrite the middle term of
`(2y^2-y-15)` as
`-6y + 5y`:

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

Factor each pair of terms:

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

Factor out the constant term:

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

Therefore, the final factorization is:

`\implies 6(y-3)(2y+5)`