Chapter 8.2, Problem 69P

Error Analysis A student factored the polynomial at the right. Describe and correct the error made in factoring.

To determine

To describe: the error made by a student while factoring a polynomial $63x^4-14x^3+35x^2$

Explanation of Solution

Given information: Factorization is given as follows.

  $\begin{array}{l}63x^4-14x^3+35x^2\\ =7x\left(9x^3-2x^2+5x\right)\end{array}$

Consider the polynomial $63x^4-14x^3+35x^2$ .

The given factorization is $63x^4-14x^3+35x^2=7x\left(9x^3-2x^2+5x\right)$

In this step, besides $7x$ , another $x$ is also common in the terms $9x^3,-2x^2,5x$ .

So, the expression $9x^3-2x^2+5x$ can be further factorized.

Hence,

In each of the terms $63x^4,-14x^3,35x^2$ , the common factor should be taken as $7x(x)=7x^2$

Therefore, $7x^2$ should be taken common instead of just $7x$

  $\begin{array}{l}63x^4-14x^3+35x^2\\ =7x^2\left(9x^2-2x+5\right)\end{array}$