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Concept explainers
(a)
The blank spaces in the given table.
(a)
![Check Mark](/static/check-mark.png)
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)
The way in which m and p are related to a and c.
(b)
![Check Mark](/static/check-mark.png)
Answer to Problem 40PPS
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)
The way in which m and p are related to b.
(c)
![Check Mark](/static/check-mark.png)
Answer to Problem 40PPS
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)
The factors of the equation.
(d)
![Check Mark](/static/check-mark.png)
Answer to Problem 40PPS
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.
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