Chapter 8.3, Problem 40PPS

(a)

To determine

The blank spaces in the given table.

Explanation of Solution

Given:

Leading coefficient = 1

Calculation:

The solution for the given statement can be obtained as:

Product of two Binomials	ax2+mx+px+c	ax2+bx+c	m x p	a x c
(2x+3) (x+4)	2x2+8x+3x+12	2x2+11x+12	24	24
(x+1) (3x+5)	3x2+5x+3x+5	3x2+8x+5	15	15
(2x-1) (4x+1)	8x2+2x-4x-1	8x2+2x-1	-8	-8
(3x+5) (4x-2)	12x2-6x+20x-10	12x2+14x-10	-20	-20

(b)

To determine

The way in which m and p are related to a and c.

Answer to Problem 40PPS

  $mp=ac$

Explanation of Solution

Given:

The given equation is:

Leading coefficient = 1

Calculation: The solution for the given statement can be obtained as:

ac is the product of the coefficients of the first and last terms.

mp is the product of the coefficients of the middle two terms when foiling.

The last two columns are mp = ac.

(c)

To determine

The way in which m and p are related to b.

Answer to Problem 40PPS

  $m+p=b$

Explanation of Solution

Given:

The given equation is:

Leading coefficient = 1

Calculation:

The solution for the given statement can be obtained as:

At the second and third columns: m + p = b.

The coefficients of the middle terms equal b. 

(d)

To determine

The factors of the equation.

Answer to Problem 40PPS

  $mp=ac,m+p=b$

Explanation of Solution

Given:

The given equation is:

Leading coefficient = 1

Calculation:

The solution for the given statement can be obtained as:

When factoring trinomials,

Two integers are m and p,

For which mp = ac and m + p = b.