Chapter 8.5, Problem 2P

a.

To determine

Factored form of $y^2-6y+8$

Answer to Problem 2P

  $y^2-6y+8=\left(y-2\right)\left(y-4\right)$

Explanation of Solution

Given:

  $y^2-6y+8$

Calculation:

Factored form:

  $\begin{array}{l}{y}^2-6y+8\\ y^2-\left(4+2\right)y+8\\ y^2-4y-2y+8\\ y\left(y-4\right)-2\left(y-4\right)\\ \left(y-2\right)\left(y-4\right)\end{array}$

b.

To determine

Can $x^2-x+2$ be factored?

Answer to Problem 2P

No

Explanation of Solution

Given:

  $x^2-x+2$

Calculation:

Factored form:

  $\begin{array}{l}{x}^2-x+2\\ x^2-\left(2-1\right)x+2\\ x^2-2x+x+2\\ x\left(x-2\right)+1\left(x+2\right)\end{array}$

Because, the x − 2 and x + 2 is not same. Hence, the $x^2-x+2$ can’t be factored