Skip to main content
Factor
Tick mark Image
Evaluate
Tick mark Image
Graph

Similar Problems from Web Search

Share

x^{4}-6x^{3}-8x^{2}+96x-128=0
To factor the expression, solve the equation where it equals to 0.
±128,±64,±32,±16,±8,±4,±2,±1
By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -128 and q divides the leading coefficient 1. List all candidates \frac{p}{q}.
x=2
Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.
x^{3}-4x^{2}-16x+64=0
By Factor theorem, x-k is a factor of the polynomial for each root k. Divide x^{4}-6x^{3}-8x^{2}+96x-128 by x-2 to get x^{3}-4x^{2}-16x+64. To factor the result, solve the equation where it equals to 0.
±64,±32,±16,±8,±4,±2,±1
By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 64 and q divides the leading coefficient 1. List all candidates \frac{p}{q}.
x=4
Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.
x^{2}-16=0
By Factor theorem, x-k is a factor of the polynomial for each root k. Divide x^{3}-4x^{2}-16x+64 by x-4 to get x^{2}-16. To factor the result, solve the equation where it equals to 0.
x=\frac{0±\sqrt{0^{2}-4\times 1\left(-16\right)}}{2}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, 0 for b, and -16 for c in the quadratic formula.
x=\frac{0±8}{2}
Do the calculations.
x=-4 x=4
Solve the equation x^{2}-16=0 when ± is plus and when ± is minus.
\left(x-2\right)\left(x+4\right)\left(x-4\right)^{2}
Rewrite the factored expression using the obtained roots.