Answer:
1. -x^2 - 15x - 1
2. -33x^7 + 10x^6 - 14x^5 + 4x^4 + 11x^2 - 5x + 32
Step-by-step explanation:
Problem 1.
How much greater is -20x^2 + 5x + 17 than -19x^2 + 20x + 18
Problem 1. Solution:
Subtract the second polynomial from the first polynomial.
-20x^2 + 5x + 17 - (-19x^2 + 20x + 18) =
To simplify the parentheses, think of the negative sign left of the parentheses as the number -1, and distribute it using the distributive property.
= -20x^2 + 5x + 17 -1(-19x^2 + 20x + 18)
We multiply -1 by each term in the parentheses.
= -20x^2 + 5x + 17 + 19x^2 - 20x - 18
Now we combine like terms. First, group each set of like terms together.
= -20x^2 + 19x^2 + 5x - 20x + 17 - 18
Now combine like terms.
= -x^2 - 15x - 1
Answer to Problem 1.: -x^2 - 15x - 1
Problem 2.
How much greater is -20x^7 + 10x^6 - 5x + 15 than 13x^7 + 14x^5 -4x^4 -11x^2 - 17
Problem 2. Solution:
Subtract the second polynomial from the first polynomial.
-20x^7 + 10x^6 - 5x + 15 - (13x^7 + 14x^5 - 4x^4 - 11x^2 - 17) =
To simplify the parentheses, think of the negative sign left of the parentheses as the number -1, and distribute it using the distributive property.
= -20x^7 + 10x^6 - 5x + 15 -1(13x^7 + 14x^5 - 4x^4 - 11x^2 - 17)
We multiply -1 by each term in the parentheses.
= -20x^7 + 10x^6 - 5x + 15 - 13x^7 - 14x^5 + 4x^4 + 11x^2 + 17
Now we combine like terms. First, group each set of like terms together.
= -20x^7 - 13x^7 + 10x^6 - 14x^5 + 4x^4 + 11x^2 - 5x + 15 + 17
Now combine like terms.
= -33x^7 + 10x^6 - 14x^5 + 4x^4 + 11x^2 - 5x + 32
Answer to Problem 2.: -33x^7 + 10x^6 - 14x^5 + 4x^4 + 11x^2 - 5x + 32
, 
and the solutions are decreasing functions.