Solve 3(2)^3x^2+2x-1)

$$3 ( 2 ) ^ { 3 } x ^ { 2 } + 2 x - 1 )$$

Evaluate

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

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$3\times 8x^{2}+2x-1$$

Multiply 3 and 8 to get 24.

$$24x^{2}+2x-1$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$24x^{2}+2x-1$$

Factor the expression by grouping. First, the expression needs to be rewritten as 24x^{2}+ax+bx-1. To find a and b, set up a system to be solved.

$$a+b=2 ab=24\left(-1\right)=-24$$

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 2.

$$a=-4 b=6$$

Rewrite 24x^{2}+2x-1 as \left(24x^{2}-4x\right)+\left(6x-1\right).

$$\left(24x^{2}-4x\right)+\left(6x-1\right)$$

Factor out 4x in 24x^{2}-4x.

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

Factor out common term 6x-1 by using distributive property.

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