Solve -3x^6+2x^6+9x^5-7x^3-1

$$-3 { x }^{ 6 } +2 { x }^{ 6 } +9 { x }^{ 5 } -7 { x }^{ 3 } -1$$

Factor

$$\left(x-1\right)\left(1+x+x^{2}+8x^{3}+8x^{4}-x^{5}\right)$$

Solution Steps

Multiply and combine like terms.

$$-x^{6}+9x^{5}-7x^{3}-1$$

By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -1 and q divides the leading coefficient -1. One such root is 1. Factor the polynomial by dividing it by x-1. Polynomial -x^{5}+8x^{4}+8x^{3}+x^{2}+x+1 is not factored since it does not have any rational roots.

$$\left(x-1\right)\left(-x^{5}+8x^{4}+8x^{3}+x^{2}+x+1\right)$$

Evaluate

$$-x^{6}+9x^{5}-7x^{3}-1$$

Solution Steps

Combine -3x^{6} and 2x^{6} to get -x^{6}.

$$-x^{6}+9x^{5}-7x^{3}-1$$