Solve 10x^2+5x-2x-1

$$10 x ^ { 2 } + 5 x - 2 x - 1$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$10x^{2}+3x-1$$

Factor the expression by grouping. First, the expression needs to be rewritten as 10x^{2}+ax+bx-1. To find a and b, set up a system to be solved.

$$a+b=3 ab=10\left(-1\right)=-10$$

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 -10.

$$-1,10 -2,5$$

Calculate the sum for each pair.

$$-1+10=9 -2+5=3$$

The solution is the pair that gives sum 3.

$$a=-2 b=5$$

Rewrite 10x^{2}+3x-1 as \left(10x^{2}-2x\right)+\left(5x-1\right).

$$\left(10x^{2}-2x\right)+\left(5x-1\right)$$

Factor out 2x in 10x^{2}-2x.

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

Factor out common term 5x-1 by using distributive property.

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

Evaluate

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

Solution Steps

Combine 5x and -2x to get 3x.

$$10x^{2}+3x-1$$