Solve x^2-13x+30-x+3

$$x ^ { 2 } - 13 x + 30 - x + 3$$

Evaluate

$$\left(x-11\right)\left(x-3\right)$$

Solution Steps

Combine -13x and -x to get -14x.

$$x^{2}-14x+30+3$$

Add 30 and 3 to get 33.

$$x^{2}-14x+33$$

Factor

$$\left(x-11\right)\left(x-3\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{2}-14x+33$$

Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+33. To find a and b, set up a system to be solved.

$$a+b=-14 ab=1\times 33=33$$

Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 33.

$$-1,-33 -3,-11$$

Calculate the sum for each pair.

$$-1-33=-34 -3-11=-14$$

The solution is the pair that gives sum -14.

$$a=-11 b=-3$$

Rewrite x^{2}-14x+33 as \left(x^{2}-11x\right)+\left(-3x+33\right).

$$\left(x^{2}-11x\right)+\left(-3x+33\right)$$

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

$$x\left(x-11\right)-3\left(x-11\right)$$

Factor out common term x-11 by using distributive property.

$$\left(x-11\right)\left(x-3\right)$$