Chapter A.2, Problem 78E

Solution

To factor completely $2x^3-16x^2+14$ .

  $2\left(x-1\right)\left(x^2-7x-7\right)$

Given:

The expression, $2x^3-16x^2+14$

Concept Used:

• Like terms are the terms that contain the same variable with similar exponents on it. Constants are like terms as well.
• In any expression, terms are separated by plus or minus signs.
• Coefficients are the constants in front of the variable terms.

Calculation:

In order to find the factor completely, first factoring the term by greatest common factor and then solving it as shown below:

  $\begin{array}{l}2x^3-16x^2+14\\ 2\left(x^3-8x^2+7\right)\\ 2\left(x-1\right)\left(x^2-7x-7\right)\end{array}$

The original expression now become

  $2\left(x-1\right)\left(x^2-7x-7\right)$