Solve 3x^2-9x+x-3

$$3 x ^ { 2 } - 9 x + x - 3$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$3x^{2}-8x-3$$

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

$$a+b=-8 ab=3\left(-3\right)=-9$$

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 -9.

$$1,-9 3,-3$$

Calculate the sum for each pair.

$$1-9=-8 3-3=0$$

The solution is the pair that gives sum -8.

$$a=-9 b=1$$

Rewrite 3x^{2}-8x-3 as \left(3x^{2}-9x\right)+\left(x-3\right).

$$\left(3x^{2}-9x\right)+\left(x-3\right)$$

Factor out 3x in 3x^{2}-9x.

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

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

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

Evaluate

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

Solution Steps

Combine -9x and x to get -8x.

$$3x^{2}-8x-3$$