Chapter 8.6, Problem 45HP

To determine

To find: All the values of k so that the polynomial can be factored using integers.

Answer to Problem 45HP

  $-15,-9,9,15$

Explanation of Solution

Given:

  $x^2+kx+14$

Calculation:

The given polynomial is $x^2+kx+14$

Comparing this with $a{x}^2+bx+c$ ,

  $a=1,b=k,c=14$

The value of $ac$ is $14$

Now, the factor pairs of 14 are

  $\begin{array}{l}1,14\\ 2,7\end{array}$

From ac method the middle term b should be equal to the sum/difference of factors pairs of ac .

So, the sum/difference of above factor pairs which is equal to ac are

  $\begin{array}{l}-1-14=-15\\ -2-7=-9\\ 1+14=15\\ 2+7=9\end{array}$

Hence, the values of k are $-15,-9,9,15$