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f(x)=(4x^2+x+-36)/(x^3-2)−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

4x2+ x−36x3−2\frac{4x^2+\:x-36}{x^3-2}

Step-by-step Solution

1

Factor the difference of cubes: a3−b3=(a−b)(a2+ab+b2)a^3-b^3 = (a-b)(a^2+ab+b^2)

4x2+x−36(x−23)(x2+23x+(2)23)\frac{4x^2+x-36}{\left(x-\sqrt[3]{2}\right)\left(x^2+\sqrt[3]{2}x+\sqrt[3]{\left(2\right)^{2}}\right)}

Final answer to the exercise

4x2+x−36(x−23)(x2+23x+(2)23)\frac{4x^2+x-36}{\left(x-\sqrt[3]{2}\right)\left(x^2+\sqrt[3]{2}x+\sqrt[3]{\left(2\right)^{2}}\right)}

Try other ways to solve this exercise

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Main Topic: Factorization

In mathematics, factorization or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original.

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4x2+ x−36x3−2 
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