# Suppose that x represents the larger of two consecutive odd integers. a. Write a polynomial that represents the smaller integer. b. Write a polynomial

Applications of integrals
Suppose that x represents the larger of two consecutive odd integers.
a. Write a polynomial that represents the smaller integer.
b. Write a polynomial that represents the sum of the two integers. Then simplify.
c. Write a polynomial that represents the product of the two integers. Then simplify.
d. Write a polynomial that represents the difference of the squares of the two integers. Then simplify

2021-04-25

Step 1
Given: x represents the larger of two consecutive odd integers
a. a polynomial which represent the smaller integer is $$x−2$$
b. a polynomial which represent the sum of two integers are x and $$x−2$$
is $$x+x−2=2x−2$$
Step 2
c. a polynomial which represent the product of two integers are
$$\displaystyle{x}{\left({x}−{2}\right)}={x}^{{{2}}}−{2}{x}$$
d. a polynomial which represent the difference of square of two integers are
$$\displaystyle{x}^{{{2}}}−{\left({x}−{2}\right)}^{{{2}}}={x}^{{{2}}}−{x}^{{{2}}}+{4}{x}−{4}={4}{x}−{4}$$