Answer:
y²(y + 3)(5y - 3)
Step-by-step explanation:
Given
5[tex]y^{4}[/tex] + 12y³ - 9y² ← factor out y² from each term
= y²(5y² + 12y - 9) ← factor the quadratic
Consider the factors of the product of the y² term and the constant term which sum to give the coefficient of the y- term
product = 5 × - 9 = - 45 and sum = + 12
The factors are + 15 and - 3
Use these factors to split the y- term
5y² + 15y - 3y - 9 ( factor the first/second and third/fourth terms )
= 5y(y + 3) - 3(y + 3) ← factor out (y + 3) from each term
= (y + 3)(5y - 3), so
5y² + 12y - 9 = (y + 3)(5y - 3)
Then
5[tex]y^{4}[/tex] + 12y³ - 9y² = y²(y + 3)(5y - 3) ← in factored form
