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

Question

asked Jul 27, 2023 90.8k views

2 Answers

Chris Hannon · Answer 1 · 2023-07-30T01:19:55+0000

Answer:

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)

Jasan · Answer 2 · 2023-08-01T12:12:05+0000

Answer:

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
, 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:

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