Chapter 8.5, Problem 51PPS

a.

To determine

To find: Determine which two factors have a product of $-6$ and sum of $1$ .

Answer to Problem 51PPS

The factors are $3$ and $-2$

Explanation of Solution

Given information:

Product $=-6$

Sum $=1$

Make a table with the different factors of $-6$ .

We need to find the sum and product of each pair of factors.

Factor $1$	Factor $2$	Product of factors	Sum of factors
$1$	$-6$	$-6$	$-5$
$-1$	$6$	$-6$	$5$
$2$	$-3$	$-6$	$-1$
$-2$	$3$	$-6$	$1$

The factors are $3$ and $-2$

Since $3+\left(-2\right)=1$ and $3\left(-2\right)=-6$ .

b.

To determine

To find: Write each factor in an empty square in the box.

Explanation of Solution

  $\begin{array}{cc}{x}^2& +3x\\ -2x& -6\end{array}$

c.

To determine

To find: The factor for each row and column of the box.

Answer to Problem 51PPS

  $\left(x+3\right)\left(x-2\right)$

Explanation of Solution

  

  $\left(x+3\right)\left(x-2\right)$

d.

To determine

To find: Describe how you would use the box method to factor $x^2-3x-40$

Explanation of Solution

Place $x^2$ in the top in the top left hand corner and place $-40$ in the lower right hand corner.

Then determine which two factors have a product of $-40$ and sum of $-3$ .

Then place these factors in the box.Then find the factor of each row and column.

The factors will be listed on the very top and far left of the box.