Question

Factor the given polynomial completely.

12y⁴-66y³+30y²

Answer 1

`12y {}^(4) - 66y {}^(3) + 30y {}^(2) \\ 6y {}^(2) (2y {}^(2) - 11y + 5) \\ 6y {}^(2) (2y {}^(2) - y - 10y + 5) \\ 6y {}^(2) (y(2y - 1) - 5(2y - 1)) \\ 6y {}^(2) (2y - 1)(y - 5)`

Answer 2

6y²(2y - 1)(y - 5)

Explanation:

12
`y^(4)` - 66y³ + 30y² ← factor out 6y² from each term

= 6y²(2y² - 11y + 5) ← factor the quadratic

consider the factors of the product of the coefficient of the y² term and the constant term which sum to give the coefficient of the y- term, that is

product = 2 × 5 = 10 and sum = - 11

the factors are - 1 and - 10

use these factors to split the y- term

2y² - y - 10y + 5 ( factor the first/second and third/fourth terms )

y(2y - 1) - 5(2y - 1) ← factor out (2y - 1) from each term

(2y - 1)(y - 5)

then

12
`y^(4)` - 66y³ + 30y² = 6y²(2y - 1)(y - 5)