deisharenae05
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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 :

Paounn

Answer:

b) [tex] b) 3x(x − 3)(x2 + 3x + 9)[/tex]

Step-by-step explanation:)

Take a factor [tex] 3x[/tex] from the expression. You're left with [tex] 3x(x^3-27) = 3x(x^3-3^3)[/tex] which is a difference of cubes. Cube differences are decomposed as a product as [tex] (a-b)(a^2+ab+b^2)[/tex] (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).

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