Chapter 7.2, Problem 48E

a.

To determine

The binomials being multiplied in the table.

Answer to Problem 48E

The binomials being multiplied in the given table are $(-4x+3)$ and $(-8x-9)$ .

Explanation of Solution

Given information: The given table is:

  $\begin{array}{lll}\hfill & -4x\hfill & 3\hfill \\ -8x\hfill & a\hfill & b\hfill \\ -9\hfill & c\hfill & d\hfill \end{array}$

Calculation:

On adding the terms given on the top of the table, one of the binomials is $(-4x+3)$ .

On adding the terms along the side of the table, other binomial is $(-8x-9)$ .

So the two binomials being multiplied are $(-4x+3)$ and $(-8x-9)$ .

b.

To determine

The signs of entries in the table.

Answer to Problem 48E

a and c will be positive while b and d will be negative.

Explanation of Solution

Given information: The given table is:

  $\begin{array}{lll}\hfill & -4x\hfill & 3\hfill \\ -8x\hfill & a\hfill & b\hfill \\ -9\hfill & c\hfill & d\hfill \end{array}$

and x>0.

Calculation:

From table,

  $\begin{array}{l}a=(-8x)\times (-4x)\\ \end{array}$

  $=32x^2$ >0 (since $x>0$ , so $x^2>0$ and $32>0$ )

b $=(-8x)\times 3$

  $=-24x$<0 (since $x>0$ and $-24<0$ )

c $=(-9)\times (-4x)$

  $=36x^2>0$ (since $x^2>0$ and $36>0$ )

d $=(-9)\times 3$

  $=-27<0$

Thus, $a,c>0$ and $b,d<0$ .