Solve -8x^3+2x^2+x

$$- 8 x ^ { 3 } + 2 x ^ { 2 } + x$$

Factor

$$-x\left(2x-1\right)\left(4x+1\right)$$

Solution Steps

Factor out x.

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

Consider -8x^{2}+2x+1. Factor the expression by grouping. First, the expression needs to be rewritten as -8x^{2}+ax+bx+1. To find a and b, set up a system to be solved.

$$a+b=2 ab=-8=-8$$

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 -8.

$$-1,8 -2,4$$

Calculate the sum for each pair.

$$-1+8=7 -2+4=2$$

The solution is the pair that gives sum 2.

$$a=4 b=-2$$

Rewrite -8x^{2}+2x+1 as \left(-8x^{2}+4x\right)+\left(-2x+1\right).

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

Factor out -4x in the first and -1 in the second group.

$$-4x\left(2x-1\right)-\left(2x-1\right)$$

Factor out common term 2x-1 by using distributive property.

$$\left(2x-1\right)\left(-4x-1\right)$$

Rewrite the complete factored expression.

$$x\left(2x-1\right)\left(-4x-1\right)$$

Evaluate

$$x+2x^{2}-8x^{3}$$