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Factor completely. 9x4 + 12x3 – 45x2 – 60x

A3x(x2 – 5)(3x – 4)

B3x(x2 – 6)(3x + 10)

C3x(x2 – 5)(3x + 4)

D3x(x2 + 5)(3x – 4)

Verified Answer :

justyn123

the answer is C if not sorry

Answer:  The correct option is

(C) \(3x(x^2-5)(3x+4).\)

Step-by-step explanation:  We are given to completely factor the following bi quadratic expression :

\(E=9x^4+12x^3-45x^2-60x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)

Since the given expression does not contain the constant term, so we will take out the x-term common and then will try to factorize the remaining cubic expression.

The factorization of expression (i) is as follows :

\(E\\\\=9x^4+12x^3-45x^2-60x\\\\=3x(3x^3+4x^2-15x-20)\\\\=3x(x^2(3x+4)-5(3x+4))\\\\=3x(x^2-5)(3x+4).\)

Thus, the required factored form of the given expression is \(3x(x^2-5)(3x+4).\)

Option (C) is CORRECT.

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