Solve (2x^2-11x)+(3x^2+10x-4)

$$( 2 x ^ { 2 } - 11 x ) + ( 3 x ^ { 2 } + 10 x - 4 )$$

Evaluate

$$\left(x-1\right)\left(5x+4\right)$$

Solution Steps

Combine 2x^{2} and 3x^{2} to get 5x^{2}.

$$5x^{2}-11x+10x-4$$

Combine -11x and 10x to get -x.

$$5x^{2}-x-4$$

Factor

$$\left(x-1\right)\left(5x+4\right)$$

Solution Steps

Multiply and combine like terms.

$$5x^{2}-x-4$$

Factor the expression by grouping. First, the expression needs to be rewritten as 5x^{2}+ax+bx-4. To find a and b, set up a system to be solved.

$$a+b=-1 ab=5\left(-4\right)=-20$$

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 -20.

$$1,-20 2,-10 4,-5$$

Calculate the sum for each pair.

$$1-20=-19 2-10=-8 4-5=-1$$

The solution is the pair that gives sum -1.

$$a=-5 b=4$$

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

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

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

$$5x\left(x-1\right)+4\left(x-1\right)$$

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

$$\left(x-1\right)\left(5x+4\right)$$