Solve 32x^5+40x^2-88x^3

$$32 x ^ { 5 } + 40 x ^ { 2 } - 88 x ^ { 3 }$$

Factor

$$8\left(2x-1\right)x^{2}\left(2x^{2}+x-5\right)$$

Solution Steps

Factor out 8.

$$8\left(4x^{5}+5x^{2}-11x^{3}\right)$$

Consider 4x^{5}+5x^{2}-11x^{3}. Factor out x^{2}.

$$x^{2}\left(4x^{3}+5-11x\right)$$

Consider 4x^{3}+5-11x. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 5 and q divides the leading coefficient 4. One such root is \frac{1}{2}. Factor the polynomial by dividing it by 2x-1.

$$\left(2x-1\right)\left(2x^{2}+x-5\right)$$

Rewrite the complete factored expression. Polynomial 2x^{2}+x-5 is not factored since it does not have any rational roots.

$$8x^{2}\left(2x-1\right)\left(2x^{2}+x-5\right)$$

Evaluate

$$8x^{2}\left(4x^{3}-11x+5\right)$$