Solve 4x^2-1x-6x-15

$$4 x ^ { 2 } - 1 x - 6 x - 15$$

Factor

$$\left(x-3\right)\left(4x+5\right)$$

Solution Steps

Multiply and combine like terms.

$$4x^{2}-7x-15$$

Factor the expression by grouping. First, the expression needs to be rewritten as 4x^{2}+ax+bx-15. To find a and b, set up a system to be solved.

$$a+b=-7 ab=4\left(-15\right)=-60$$

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 -60.

$$1,-60 2,-30 3,-20 4,-15 5,-12 6,-10$$

Calculate the sum for each pair.

$$1-60=-59 2-30=-28 3-20=-17 4-15=-11 5-12=-7 6-10=-4$$

The solution is the pair that gives sum -7.

$$a=-12 b=5$$

Rewrite 4x^{2}-7x-15 as \left(4x^{2}-12x\right)+\left(5x-15\right).

$$\left(4x^{2}-12x\right)+\left(5x-15\right)$$

Factor out 4x in the first and 5 in the second group.

$$4x\left(x-3\right)+5\left(x-3\right)$$

Factor out common term x-3 by using distributive property.

$$\left(x-3\right)\left(4x+5\right)$$

Evaluate

$$\left(x-3\right)\left(4x+5\right)$$

Solution Steps

Combine -x and -6x to get -7x.

$$4x^{2}-7x-15$$