Solve 6^x^2-23x-4

$${ 6 }^{ } { x }^{ 2 } -23x-4$$

Factor

$$\left(x-4\right)\left(6x+1\right)$$

Solution Steps

Multiply and combine like terms.

$$6x^{2}-23x-4$$

Factor the expression by grouping. First, the expression needs to be rewritten as 6x^{2}+ax+bx-4. To find a and b, set up a system to be solved.

$$a+b=-23 ab=6\left(-4\right)=-24$$

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 -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 -23.

$$a=-24 b=1$$

Rewrite 6x^{2}-23x-4 as \left(6x^{2}-24x\right)+\left(x-4\right).

$$\left(6x^{2}-24x\right)+\left(x-4\right)$$

Factor out 6x in 6x^{2}-24x.

$$6x\left(x-4\right)+x-4$$

Factor out common term x-4 by using distributive property.

$$\left(x-4\right)\left(6x+1\right)$$

Evaluate

$$\left(x-4\right)\left(6x+1\right)$$

Solution Steps

Calculate 6 to the power of 1 and get 6.

$$6x^{2}-23x-4$$