Solve 40ax^2+224ax-96a

$$40 a x ^ { 2 } + 224 a x - 96 a$$

Factor

$$8a\left(5x-2\right)\left(x+6\right)$$

Solution Steps

Factor out 8.

$$8\left(5ax^{2}+28ax-12a\right)$$

Consider 5ax^{2}+28ax-12a. Factor out a.

$$a\left(5x^{2}+28x-12\right)$$

Consider 5x^{2}+28x-12. Factor the expression by grouping. First, the expression needs to be rewritten as 5x^{2}+px+qx-12. To find p and q, set up a system to be solved.

$$p+q=28 pq=5\left(-12\right)=-60$$

Since pq is negative, p and q have the opposite signs. Since p+q is positive, the positive number has greater absolute value than the negative. 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 28.

$$p=-2 q=30$$

Rewrite 5x^{2}+28x-12 as \left(5x^{2}-2x\right)+\left(30x-12\right).

$$\left(5x^{2}-2x\right)+\left(30x-12\right)$$

Factor out x in the first and 6 in the second group.

$$x\left(5x-2\right)+6\left(5x-2\right)$$

Factor out common term 5x-2 by using distributive property.

$$\left(5x-2\right)\left(x+6\right)$$

Rewrite the complete factored expression.

$$8a\left(5x-2\right)\left(x+6\right)$$

Evaluate

$$8a\left(5x-2\right)\left(x+6\right)$$