Solve xx-7x+6

$$xx-7x+6$$

Factor

$$\left(x-6\right)\left(x-1\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{2}-7x+6$$

Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+6. To find a and b, set up a system to be solved.

$$a+b=-7 ab=1\times 6=6$$

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 6.

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

Calculate the sum for each pair.

$$-1-6=-7 -2-3=-5$$

The solution is the pair that gives sum -7.

$$a=-6 b=-1$$

Rewrite x^{2}-7x+6 as \left(x^{2}-6x\right)+\left(-x+6\right).

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

Factor out x in the first and -1 in the second group.

$$x\left(x-6\right)-\left(x-6\right)$$

Factor out common term x-6 by using distributive property.

$$\left(x-6\right)\left(x-1\right)$$

Evaluate

$$\left(x-6\right)\left(x-1\right)$$

Solution Steps

Multiply x and x to get x^{2}.

$$x^{2}-7x+6$$