Question

Factor the polynomial.3x^6y^2+81y^2

A)3y^2(x^2+3)(x^4-3x^2-9)
B)3y^2(x^2-3)(x^4+3×+9)
C)prime polynomial
D)3y^2(x^2+3)(x^4-3x^2+9)

Answer 1

3x⁶y²+81y² =
3y²(x⁶+27) =
3y²((x²)³+3³)=
3y²(x²+3)(x⁴-3x²+9)

Answer: D.

Answer 2

Answer is choice D

The reason why is...
3x^6y^2 + 81y^2 = 3y^2(x^6 + 27)
3x^6y^2 + 81y^2 = 3y^2((x^2)^3 + 3^3)
3x^6y^2 + 81y^2 = 3y^2(x^2 + 3)((x^2)^2 - (x^2)*3 + 3^2)
3x^6y^2 + 81y^2 = 3y^2(x^2 + 3)(x^4 - 3x^2 + 9)