Solve 1-x^2+6x-9

$$1 - x ^ { 2 } + 6 x - 9$$

Factor

$$\left(2-x\right)\left(x-4\right)$$

Solution Steps

Multiply and combine like terms.

$$-x^{2}+6x-8$$

Factor the expression by grouping. First, the expression needs to be rewritten as -x^{2}+ax+bx-8. To find a and b, set up a system to be solved.

$$a+b=6 ab=-\left(-8\right)=8$$

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 8.

$$1,8 2,4$$

Calculate the sum for each pair.

$$1+8=9 2+4=6$$

The solution is the pair that gives sum 6.

$$a=4 b=2$$

Rewrite -x^{2}+6x-8 as \left(-x^{2}+4x\right)+\left(2x-8\right).

$$\left(-x^{2}+4x\right)+\left(2x-8\right)$$

Factor out -x in the first and 2 in the second group.

$$-x\left(x-4\right)+2\left(x-4\right)$$

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

$$\left(x-4\right)\left(-x+2\right)$$

Evaluate

$$\left(2-x\right)\left(x-4\right)$$

Solution Steps

Subtract 9 from 1 to get -8.

$$-8-x^{2}+6x$$