Solve x-x^2+4x-4

$$x - x ^ { 2 } + 4 x - 4$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$-x^{2}+5x-4$$

Factor the expression by grouping. First, the expression needs to be rewritten as -x^{2}+ax+bx-4. To find a and b, set up a system to be solved.

$$a+b=5 ab=-\left(-4\right)=4$$

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. 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 -x^{2}+5x-4 as \left(-x^{2}+4x\right)+\left(x-4\right).

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

Factor out -x in -x^{2}+4x.

$$-x\left(x-4\right)+x-4$$

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

$$\left(x-4\right)\left(-x+1\right)$$

Evaluate

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

Solution Steps

Combine x and 4x to get 5x.

$$5x-x^{2}-4$$