Solve p(x)=2x^3+24x^2-56x | Microsoft Math Solver

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2\left(x^{3}+12x^{2}-28x\right)

Factor out 2.

x\left(x^{2}+12x-28\right)

Consider x^{3}+12x^{2}-28x. Factor out x.

a+b=12 ab=1\left(-28\right)=-28

Consider x^{2}+12x-28. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-28. To find a and b, set up a system to be solved.

-1,28 -2,14 -4,7

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -28.

-1+28=27 -2+14=12 -4+7=3

Calculate the sum for each pair.

a=-2 b=14

The solution is the pair that gives sum 12.

\left(x^{2}-2x\right)+\left(14x-28\right)

Rewrite x^{2}+12x-28 as \left(x^{2}-2x\right)+\left(14x-28\right).

x\left(x-2\right)+14\left(x-2\right)

Factor out x in the first and 14 in the second group.

\left(x-2\right)\left(x+14\right)

Factor out common term x-2 by using distributive property.

2x\left(x-2\right)\left(x+14\right)

Rewrite the complete factored expression.