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

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

Factor

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

Solution Steps

Multiply and combine like terms.

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

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.

$$a+b=-1 ab=-2\times 3=-6$$

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 -1.

$$a=2 b=-3$$

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

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

Factor out 2x in the first and 3 in the second group.

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

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

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

Evaluate

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

Solution Steps

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

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