Question

Which product of prime polynomials is equivalent to 3x^4 - 81x?

a) 3x(x − 3)(x2 – 3x - 9)
b) 3x(x − 3)(x2 + 3x + 9)
c) 3x(x - 3)(x - 3)(x + 3)
d) 3x(x − 3)(x + 3)(x + 3)

Answer 1

b)
`b) 3x(x − 3)(x2 + 3x + 9)`

Step-by-step explanation:)

Take a factor
`3x` from the expression. You're left with
`3x(x^3-27) = 3x(x^3-3^3)` which is a difference of cubes. Cube differences are decomposed as a product as
`(a-b)(a^2+ab+b^2)` (an easy way to remember that is that you already have the minus in the first bracket to cancel out terms, so they're all pluses in the second).