Solve (9)4x^2-8x-5

$$( 9 ) 4 x ^ { 2 } - 8 x - 5$$

Factor

$$\left(2x-1\right)\left(18x+5\right)$$

Solution Steps

Multiply and combine like terms.

$$36x^{2}-8x-5$$

Factor the expression by grouping. First, the expression needs to be rewritten as 36x^{2}+ax+bx-5. To find a and b, set up a system to be solved.

$$a+b=-8 ab=36\left(-5\right)=-180$$

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 -180.

$$1,-180 2,-90 3,-60 4,-45 5,-36 6,-30 9,-20 10,-18 12,-15$$

Calculate the sum for each pair.

$$1-180=-179 2-90=-88 3-60=-57 4-45=-41 5-36=-31 6-30=-24 9-20=-11 10-18=-8 12-15=-3$$

The solution is the pair that gives sum -8.

$$a=-18 b=10$$

Rewrite 36x^{2}-8x-5 as \left(36x^{2}-18x\right)+\left(10x-5\right).

$$\left(36x^{2}-18x\right)+\left(10x-5\right)$$

Factor out 18x in the first and 5 in the second group.

$$18x\left(2x-1\right)+5\left(2x-1\right)$$

Factor out common term 2x-1 by using distributive property.

$$\left(2x-1\right)\left(18x+5\right)$$

Evaluate

$$\left(2x-1\right)\left(18x+5\right)$$

Solution Steps

Multiply 9 and 4 to get 36.

$$36x^{2}-8x-5$$