Solve m^2-5m+2m-10

$$m ^ { 2 } - 5 m + 2 m - 10$$

Factor

$$\left(m-5\right)\left(m+2\right)$$

Solution Steps

Multiply and combine like terms.

$$m^{2}-3m-10$$

Factor the expression by grouping. First, the expression needs to be rewritten as m^{2}+am+bm-10. To find a and b, set up a system to be solved.

$$a+b=-3 ab=1\left(-10\right)=-10$$

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 -10.

$$1,-10 2,-5$$

Calculate the sum for each pair.

$$1-10=-9 2-5=-3$$

The solution is the pair that gives sum -3.

$$a=-5 b=2$$

Rewrite m^{2}-3m-10 as \left(m^{2}-5m\right)+\left(2m-10\right).

$$\left(m^{2}-5m\right)+\left(2m-10\right)$$

Factor out m in the first and 2 in the second group.

$$m\left(m-5\right)+2\left(m-5\right)$$

Factor out common term m-5 by using distributive property.

$$\left(m-5\right)\left(m+2\right)$$

Evaluate

$$\left(m-5\right)\left(m+2\right)$$

Solution Steps

Combine -5m and 2m to get -3m.

$$m^{2}-3m-10$$