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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)

Respuesta :

allisonhaines
Since 4x^2 is the GCF of the terms in the polynomial, that would have to be the value outside of the parenthesis in the product of prime polynomials, so the answer would be the second expression, 4x^2(2x-3)(x+6).

Answer: Second option is correct.

Step-by-step explanation:

Since we have given that

[tex]8x^4 + 36x^3-72x^2[/tex]

We need to solve the polynomials into product of prime polynomials :

1) Taking common factor i.e. 4x

[tex]8x^4 + 36x^3-72x^2\\\\=4x^2(2x^2+9x-18)[/tex]

2) Now, we will split the middle term of quadratic equation:

[tex]2x^2+9x-18\\\\=2x^2+12x-3x-18\\\\=2x(x+6)-3(x+6)\\\\=(2x-3)(x+6)[/tex]

3) Now, combine all the expression :

[tex]4x^2(x+6)(2x-3)[/tex]

Hence, Second option is correct.

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