Solve 2x^3-16x^2+14x

$$2 { x }^{ 3 } -16 { x }^{ 2 } +14x$$

Factor

$$2x\left(x-7\right)\left(x-1\right)$$

Solution Steps

Factor out 2.

$$2\left(x^{3}-8x^{2}+7x\right)$$

Consider x^{3}-8x^{2}+7x. Factor out x.

$$x\left(x^{2}-8x+7\right)$$

Consider x^{2}-8x+7. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+7. To find a and b, set up a system to be solved.

$$a+b=-8 ab=1\times 7=7$$

Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. The only such pair is the system solution.

$$a=-7 b=-1$$

Rewrite x^{2}-8x+7 as \left(x^{2}-7x\right)+\left(-x+7\right).

$$\left(x^{2}-7x\right)+\left(-x+7\right)$$

Factor out x in the first and -1 in the second group.

$$x\left(x-7\right)-\left(x-7\right)$$

Factor out common term x-7 by using distributive property.

$$\left(x-7\right)\left(x-1\right)$$

Rewrite the complete factored expression.

$$2x\left(x-7\right)\left(x-1\right)$$

Evaluate

$$2x\left(x-7\right)\left(x-1\right)$$