Solve 15x^3-87x^2-18x

$$15 x ^ { 3 } - 87 x ^ { 2 } - 18 x$$

Factor

$$3x\left(x-6\right)\left(5x+1\right)$$

Solution Steps

Factor out 3.

$$3\left(5x^{3}-29x^{2}-6x\right)$$

Consider 5x^{3}-29x^{2}-6x. Factor out x.

$$x\left(5x^{2}-29x-6\right)$$

Consider 5x^{2}-29x-6. Factor the expression by grouping. First, the expression needs to be rewritten as 5x^{2}+ax+bx-6. To find a and b, set up a system to be solved.

$$a+b=-29 ab=5\left(-6\right)=-30$$

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 -30.

$$1,-30 2,-15 3,-10 5,-6$$

Calculate the sum for each pair.

$$1-30=-29 2-15=-13 3-10=-7 5-6=-1$$

The solution is the pair that gives sum -29.

$$a=-30 b=1$$

Rewrite 5x^{2}-29x-6 as \left(5x^{2}-30x\right)+\left(x-6\right).

$$\left(5x^{2}-30x\right)+\left(x-6\right)$$

Factor out 5x in 5x^{2}-30x.

$$5x\left(x-6\right)+x-6$$

Factor out common term x-6 by using distributive property.

$$\left(x-6\right)\left(5x+1\right)$$

Rewrite the complete factored expression.

$$3x\left(x-6\right)\left(5x+1\right)$$

Evaluate

$$3x\left(x-6\right)\left(5x+1\right)$$