Solve 8quad3x^4-27x^3-64x^2-14x-x^4

$$8 \quad 3 x ^ { 4 } - 27 x ^ { 3 } - 64 x ^ { 2 } - 14 x - x ^ { 4 }$$

Evaluate

$$x\left(x+1\right)\left(23x^{2}-50x-14\right)$$

Solution Steps

Multiply 8 and 3 to get 24.

$$24x^{4}-27x^{3}-64x^{2}-14x-x^{4}$$

Combine 24x^{4} and -x^{4} to get 23x^{4}.

$$23x^{4}-27x^{3}-64x^{2}-14x$$

Factor

$$x\left(x+1\right)\left(23x^{2}-50x-14\right)$$

Solution Steps

Factor out x.

$$x\left(24x^{3}-27x^{2}-64x-14-x^{3}\right)$$

Consider 24x^{3}-27x^{2}-64x-14-x^{3}. Multiply and combine like terms.

$$23x^{3}-27x^{2}-64x-14$$

Consider 23x^{3}-27x^{2}-64x-14. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -14 and q divides the leading coefficient 23. One such root is -1. Factor the polynomial by dividing it by x+1.

$$\left(x+1\right)\left(23x^{2}-50x-14\right)$$

Rewrite the complete factored expression. Polynomial 23x^{2}-50x-14 is not factored since it does not have any rational roots.

$$x\left(x+1\right)\left(23x^{2}-50x-14\right)$$