Question

Which product of prime polynomials is equivalent to 8x4 36x3 – 72x2? 4x(2x – 3)(x2 6) 4x2(2x – 3)(x 6) 2x(2x – 3)(2x2 6) 2x(2x 3)(x2 – 6).

Answer 1

You can do defactoring of the given polynomial in simpler polynomials to get it as a  product of prime polynomials (assuming that it itself is not a prime polynomial)

The product of prime polynomial which forms the given polynomial is given by

Option B: $4x^2(2x-3)(x+6)$

What are prime polynomials?

Those polynomials with integer coefficients that cannot be factored further, with factors of lower degree and integer coefficients are called prime polynomial.

(it is necessary that no factors exists having their coefficients are still integers and they're of lower degree)

How to know which prime polynomials' product is equivalent to the given polynomial?

We can try defactoring the given polynomial in simpler polynomials.

The given polynomial is

$8x^4 + 36x^3 - 72x^2$

Factorizing it can be done as

$\begin{aligned} 8x^4 + 36x^3 - 72x^2 &= 4x^2(2x^2 + 9x - 18)\\&= 4x^2(2x^2 + 12x - 3x - 18)\\&= 4x^2(2x(x+6) -3(x+60))\\&= 4x^2(x+6)(2x-3)\\&=4x^2(2x-3)(x+6)\\\end{aligned}$

Thus,

The product of prime polynomial which forms the given polynomial is given by

Option B: $4x^2(2x-3)(x+6)$

Learn more about prime polynomials here:

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