Solve (2x^2-5x-3)+(x-3)

$$( 2 x ^ { 2 } - 5 x - 3 ) + ( x - 3 )$$

Evaluate

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

Solution Steps

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

$$2x^{2}-4x-3-3$$

Subtract 3 from -3 to get -6.

$$2x^{2}-4x-6$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$2x^{2}-4x-6$$

Factor out 2.

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

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

$$a+b=-2 ab=1\left(-3\right)=-3$$

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. The only such pair is the system solution.

$$a=-3 b=1$$

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

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

Factor out x in x^{2}-3x.

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

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

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

Rewrite the complete factored expression.

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