Solve 16x^3+10x^2-6x

$$16 x ^ { 3 } + 10 x ^ { 2 } - 6 x$$

Factor

$$2x\left(8x-3\right)\left(x+1\right)$$

Solution Steps

Factor out 2.

$$2\left(8x^{3}+5x^{2}-3x\right)$$

Consider 8x^{3}+5x^{2}-3x. Factor out x.

$$x\left(8x^{2}+5x-3\right)$$

Consider 8x^{2}+5x-3. Factor the expression by grouping. First, the expression needs to be rewritten as 8x^{2}+ax+bx-3. To find a and b, set up a system to be solved.

$$a+b=5 ab=8\left(-3\right)=-24$$

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 -24.

$$-1,24 -2,12 -3,8 -4,6$$

Calculate the sum for each pair.

$$-1+24=23 -2+12=10 -3+8=5 -4+6=2$$

The solution is the pair that gives sum 5.

$$a=-3 b=8$$

Rewrite 8x^{2}+5x-3 as \left(8x^{2}-3x\right)+\left(8x-3\right).

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

Factor out x in 8x^{2}-3x.

$$x\left(8x-3\right)+8x-3$$

Factor out common term 8x-3 by using distributive property.

$$\left(8x-3\right)\left(x+1\right)$$

Rewrite the complete factored expression.

$$2x\left(8x-3\right)\left(x+1\right)$$

Evaluate

$$2x\left(8x-3\right)\left(x+1\right)$$