Solve m^4-5m^3+4m^2

$$m ^ { 4 } - 5 m ^ { 3 } + 4 m ^ { 2 }$$

Factor

$$\left(m-4\right)\left(m-1\right)m^{2}$$

Solution Steps

Factor out m^{2}.

$$m^{2}\left(m^{2}-5m+4\right)$$

Consider m^{2}-5m+4. Factor the expression by grouping. First, the expression needs to be rewritten as m^{2}+am+bm+4. To find a and b, set up a system to be solved.

$$a+b=-5 ab=1\times 4=4$$

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 4.

$$-1,-4 -2,-2$$

Calculate the sum for each pair.

$$-1-4=-5 -2-2=-4$$

The solution is the pair that gives sum -5.

$$a=-4 b=-1$$

Rewrite m^{2}-5m+4 as \left(m^{2}-4m\right)+\left(-m+4\right).

$$\left(m^{2}-4m\right)+\left(-m+4\right)$$

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

$$m\left(m-4\right)-\left(m-4\right)$$

Factor out common term m-4 by using distributive property.

$$\left(m-4\right)\left(m-1\right)$$

Rewrite the complete factored expression.

$$m^{2}\left(m-4\right)\left(m-1\right)$$

Evaluate

$$\left(m-4\right)\left(m-1\right)m^{2}$$