Solve 2x^2-2x-3x-3

$$2 x ^ { 2 } - 2 x - 3 x - 3$$

Factor

$$\left(x-3\right)\left(2x+1\right)$$

Solution Steps

Multiply and combine like terms.

$$2x^{2}-5x-3$$

Factor the expression by grouping. First, the expression needs to be rewritten as 2x^{2}+ax+bx-3. To find a and b, set up a system to be solved.

$$a+b=-5 ab=2\left(-3\right)=-6$$

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 -6.

$$1,-6 2,-3$$

Calculate the sum for each pair.

$$1-6=-5 2-3=-1$$

The solution is the pair that gives sum -5.

$$a=-6 b=1$$

Rewrite 2x^{2}-5x-3 as \left(2x^{2}-6x\right)+\left(x-3\right).

$$\left(2x^{2}-6x\right)+\left(x-3\right)$$

Factor out 2x in 2x^{2}-6x.

$$2x\left(x-3\right)+x-3$$

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

$$\left(x-3\right)\left(2x+1\right)$$

Evaluate

$$\left(x-3\right)\left(2x+1\right)$$

Solution Steps

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

$$2x^{2}-5x-3$$