Question

Factor completely 9x3 36x2 − x − 4. (3x 4)(3x − 4)(x 1) (3x 1)(3x − 1)(x 4) (9x2 − 1)(x 4) (3x 1)(3x − 1)(x − 4).

Answer 1

The factor of the provided polynomial after the factorization process are similar to option B, which is

$(x+4)(3x+1)(3x-1)$

How to find the factor of polynomial?

The factor of a polynomial is the terms in linear or equation form, which are when multiplied together, give the original polynomial equation as result.

Find these factors by taking out the common factors.

The given polynomial equation in the problem is,

$9x^3 +36x^2 - x - 4$

The above equation has the unknown variable x and the highest power of this unknown variable is 3.

Take out the highest common factor 9x², which can divide each term of the first two terms of equation (9x³, 36x²). Thus,

$9x^2(x +4) - x - 4$

Take out the highest common factor -1 from the second two terms as,

$9x^2(x +4) -1( x + 4)$

Now take out the common group (x+4) as,

$(x +4) ( 9x^2 -1)$

The second group can be rewritten using the difference of square formula as,

$(x +4) ( (3x)^2 -1^2)\\(x+4)(3x+1)(3x-1)$

Thus, the factor of the provided polynomial after the factorization process are similar to option B, which is

$(x+4)(3x+1)(3x-1)$

Learn more about factor of polynomial here;

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