Chapter SH, Problem 14.8.5EP

To determine

To factor: the given polynomial

Answer to Problem 14.8.5EP

The required result is $\left(x-2\right)\left(x+4\right)$ .

Explanation of Solution

Given: $x^2+2x-8$

Calculation:

Write the trinomial as the product of two binomials.

Product of first terms is $x^2$ .

  $x^2+2x-8=\left(x+?\right)\left(x+?\right)$

Now find the two terms whose product must be $-8$ .

Try several factors of $-8$ so that sum of the product of outer and inner terms must be $+2x$ .

Try the factors $2,-4$ .

  $\begin{array}{l}\left(x+2\right)\left(x-4\right)=x^2+2x-4x-8\\ =x^2-2x-8\end{array}$

It is not true.

Try the factor $-2,4$ .

  $\begin{array}{l}\left(x-2\right)\left(x+4\right)=x^2-2x+4x-8\\ =x^2+2x-8\end{array}$

It is true.

Hence, the result is $\left(x-2\right)\left(x+4\right)$ .

Conclusion:

Hence, the factorization is $\left(x-2\right)\left(x+4\right)$ .