Solve s^2-6s-s+6

$$s ^ { 2 } - 6 s - s + 6$$

Factor

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

Solution Steps

Multiply and combine like terms.

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

Factor the expression by grouping. First, the expression needs to be rewritten as s^{2}+as+bs+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 s^{2}-7s+6 as \left(s^{2}-6s\right)+\left(-s+6\right).

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

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

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

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

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

Evaluate

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

Solution Steps

Combine -6s and -s to get -7s.

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