Solve (5x^2-5x+26)+(8x^2+9x-70)

$$(5 { x }^{ 2 } -5x+26)+(8 { x }^{ 2 } +9x-70)$$

Evaluate

$$\left(13x-22\right)\left(x+2\right)$$

Solution Steps

Combine 5x^{2} and 8x^{2} to get 13x^{2}.

$$13x^{2}-5x+26+9x-70$$

Combine -5x and 9x to get 4x.

$$13x^{2}+4x+26-70$$

Subtract 70 from 26 to get -44.

$$13x^{2}+4x-44$$

Factor

$$\left(13x-22\right)\left(x+2\right)$$

Solution Steps

Multiply and combine like terms.

$$13x^{2}+4x-44$$

Factor the expression by grouping. First, the expression needs to be rewritten as 13x^{2}+ax+bx-44. To find a and b, set up a system to be solved.

$$a+b=4 ab=13\left(-44\right)=-572$$

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 -572.

$$-1,572 -2,286 -4,143 -11,52 -13,44 -22,26$$

Calculate the sum for each pair.

$$-1+572=571 -2+286=284 -4+143=139 -11+52=41 -13+44=31 -22+26=4$$

The solution is the pair that gives sum 4.

$$a=-22 b=26$$

Rewrite 13x^{2}+4x-44 as \left(13x^{2}-22x\right)+\left(26x-44\right).

$$\left(13x^{2}-22x\right)+\left(26x-44\right)$$

Factor out x in the first and 2 in the second group.

$$x\left(13x-22\right)+2\left(13x-22\right)$$

Factor out common term 13x-22 by using distributive property.

$$\left(13x-22\right)\left(x+2\right)$$