SOLUTION: Hello, I need help with this 3 part problem. I have no clue what to do. Thank you so much for all your help. here is the problem A) Together Steve and Heather�s ages add up t

Question 290512: Hello,
I need help with this 3 part problem. I have no clue what to do. Thank you so much for all your help.
here is the problem
A) Together Steve and Heather�s ages add up to be ten. If we let "x" be Steve�s age, setup the polynomial describing Heather�s age (as a function, or dependent, of Steve's. The answer should fill in the blank �Heather�s age is _____�, without any equal sign within it. How many terms does your expression have? What type of polynomial is it?
B) The product (multiplication) of Steve and Heather�s ages (yes, the same Steve and Heather as in problem #1) is 21. Combining with the information in part A, setup the new expression. Do not simplify it.
C) Expand and simplify (by combining like terms) the above factoring expression. Which property do you use to expand it? Put the resulting expression in the format such that the right-hand side of the equal sign is zero. How many terms does the left-hand side have? What type of polynomial is it?

thank you again
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
First of all, it is not a good idea to use x for steve's age
It is better to use s for Steve and h for Heather. It is easy to confuse x and y but not so easy to confuse s and h.
x+h=10
for Together Steve and Heather�s ages add up to be ten.
h=10-x
If we let "x" be Steve�s age, setup the polynomial describing Heather�s age (as a function, or dependent, of Steve's.
The problem is poorly written.
At one moment it is talking about polynomials, expressions and functions and talking as if they are one thing.
The function that we wrote for heather's age is not the same as the expression that we wrote for steve and heather's age.
Expressions have no equal sign functions and equations do.
The expression for heather's age is 10-x
There are two terms in the expressions- a variable and a constant.
The function that we set up has three terms h,x and 10 the constant.
h=10-x
The polynomial 10-x is a one variable polynomial with one variable and one constant. It of the first degree.
but the function h=10-x has three terms two variables and one constant.
It is also of the first degree.
It is a first degree two variable function.

h*x=21
h+x=10
one is 7 and and the other is 3
if we want to solve for heather's age
we plug in 10-h for x
h*(10-h)=21
10h-h^2=21
It is now quadratic of degree 2
-h^2+10h-21=0
multiply by -1
or
add inverses to both sides
h^2-10h+21=0
(h-7)*(h-3)=0
h=7 and 3
I don't like the problem because it is confusing terms.
Any questions?
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