Chapter 8.6, Problem 58PFA

a.

To determine

To factor: The polynomial $x^2-7x+10$

Answer to Problem 58PFA

  $\left(x-5\right)\left(x-2\right)$

Explanation of Solution

Given:

  $x^2-7x+10$

Calculation:

The given expression is $x^2-7x+10$

Write the middle term $-7x$ as $-5x-2x$

  $x^2-5x-2x+10$

Make groups as shown below

  $\left(x^2-5x\right)\left(-2x+10\right)$

Factored out the GCF from each group

  $x\left(x-5\right)-2\left(x-5\right)$

Factored out the common term

  $\left(x-5\right)\left(x-2\right)$

b.

To determine

To factor: The polynomial $3x^2-6x+3$

Answer to Problem 58PFA

  $3{\left(x-1\right)}^2$

Explanation of Solution

Given:

  $3x^2-6x+3$

Calculation:

The given expression is $3x^2-6x+3$

Write the middle term $-6x$ as $-3x-3x$

  $3x^2-3x-3x+3$

Make groups as shown below

  $\left(3x^2-3x\right)+\left(-3x+3\right)$

Factored out the GCF from each group

  $3x\left(x-1\right)-3\left(x-1\right)$

Factored out the common term

  $\left(3x-3\right)\left(x-1\right)$

Factored out the GCF from the first factor

  $\begin{array}{l}3\left(x-1\right)\left(x-1\right)\\ =3{\left(x-1\right)}^2\end{array}$