Chapter SH, Problem 14.8.1EP

To determine

To factor: the given expression

Answer to Problem 14.8.1EP

The required result is $\left(x+3\right)\left(x+5\right)$ .

Explanation of Solution

Given: $x^2+8x+15$

Calculation:

Write the trinomial as the product of two binomials.

Product of first terms is $x^2$ .

  $x^2+8x+15=\left(x+?\right)\left(x+?\right)$

Now find the two terms whose product must be $15$ .

Try several factors of $15$ so that sum of the product of outer and inner terms must be $8x$ .

Try the factors $1,15$

  $\begin{array}{l}\left(x+15\right)\left(x+15\right)=x^2+x+15x+15\\ =x^2+16x+15\end{array}$

It is not true.

Try the factor $3,5$ .

  $\begin{array}{l}\left(x+3\right)\left(x+5\right)=x^2+3x+5x+15\\ =x^2+8x+15\end{array}$

It is true.

Hence, the result is $\left(x+3\right)\left(x+5\right)$

Conclusion:

Hence, the required result is $\left(x+3\right)\left(x+5\right)$ .