Chapter SH, Problem 14.8.3EP

To determine

To factor: the given polynomial

Answer to Problem 14.8.3EP

The required result is $\left(x-1\right)\left(x+6\right)$ .

Explanation of Solution

Given: $x^2+5x-6$

Calculation:

Write the trinomial as the product of two binomials.

Product of first terms is $x^2$ .

  $x^2+5x-6=\left(x+?\right)\left(x+?\right)$

Now find the two terms whose product must be $-6$ .

Try several factors of $-6$ so that sum of the product of outer and inner terms must be $5x$ .

Try the factors $1,-6$

  $\begin{array}{l}\left(x+1\right)\left(x-6\right)=x^2+x-6x-6\\ =x^2-5x-6\end{array}$

It is not true.

Try the factor $-1,6$ .

  $\begin{array}{l}\left(x-1\right)\left(x+6\right)=x^2-x+6x-6\\ =x^2+5x-6\end{array}$

It is true.

Hence, the result is $\left(x-1\right)\left(x+6\right)$ .

Conclusion:

Hence, the factorization is $\left(x-1\right)\left(x+6\right)$ .