Chapter 8.6, Problem 61PFA

To determine

To find: A common factor between the polynomials.

Answer to Problem 61PFA

No common term

Explanation of Solution

Given:

  $4x^2+5x+9\text{ and }{x}^2-4x+4$

Calculation:

Find the factors of the polynomial $4x^2+5x+9$

This can be factored because it is a prime polynomial.

Now, find the factors of the polynomial $x^2-4x+4$

Write the middle term $-4x=-2x=2x$

  $x^2-2x-2x+4$

Make groups as shown below

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

Factored out the GCF from each group

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

Factored out the common term

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

The first polynomial can’t be written in factored form and the second polynomial can be written in factored form as ${\left(x-2\right)}^2$

Hence, there is no common term other than 1 between the given polynomials.