Solve 6p^3-2p^2-8p

$$6 p ^ { 3 } - 2 p ^ { 2 } - 8 p$$

Factor

$$2p\left(3p-4\right)\left(p+1\right)$$

Solution Steps

Factor out 2.

$$2\left(3p^{3}-p^{2}-4p\right)$$

Consider 3p^{3}-p^{2}-4p. Factor out p.

$$p\left(3p^{2}-p-4\right)$$

Consider 3p^{2}-p-4. Factor the expression by grouping. First, the expression needs to be rewritten as 3p^{2}+ap+bp-4. To find a and b, set up a system to be solved.

$$a+b=-1 ab=3\left(-4\right)=-12$$

Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -12.

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

Calculate the sum for each pair.

$$1-12=-11 2-6=-4 3-4=-1$$

The solution is the pair that gives sum -1.

$$a=-4 b=3$$

Rewrite 3p^{2}-p-4 as \left(3p^{2}-4p\right)+\left(3p-4\right).

$$\left(3p^{2}-4p\right)+\left(3p-4\right)$$

Factor out p in 3p^{2}-4p.

$$p\left(3p-4\right)+3p-4$$

Factor out common term 3p-4 by using distributive property.

$$\left(3p-4\right)\left(p+1\right)$$

Rewrite the complete factored expression.

$$2p\left(3p-4\right)\left(p+1\right)$$

Evaluate

$$2p\left(3p-4\right)\left(p+1\right)$$