A rectangle has sides measuring (2x + 7) units and (5x + 9) units.
Part A: What is the expression that represents the area of the rectangle? Show your work to receive full credit. (4 points)
Part B: What are the degree and classification of the expression obtained in Part A? (3 points)
Part C: How does Part A demonstrate the closure property for polynomials? (3 points)
Can someone help me?

- anonymous

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- anonymous

??

- anonymous

@zepdrix

- anonymous

help

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## More answers

- anonymous

PLS

- anonymous

@freckles

- phi

what is the formula for the area of a rectangle?

- anonymous

yay phi

- anonymous

its length times the width so so assuming (2x + 7) is the length and (5x + 9) is the width, the expression would be A=(2x + 7)(5x + 9)

- anonymous

i got that for part A

- phi

they probably want you to expand it (FOIL if you learned that)

- anonymous

ive never learned that,no

- phi

did you learn how to multiply two binomials
?

- anonymous

yes i think so

- anonymous

want me to?

- phi

FOIL is to remember
First 2x*5x
Outer 2x*9
Inner 7*5x
Last 7*9
or
10x^2 + 18x+35x+63
and finally
10x^2 +53x+63

- anonymous

yea thats what i got

- anonymous

is that part of Part A?

- phi

yes, that is part A. (They want you to show your work... I assume you did)

- anonymous

yay i got part a, so can you help with part B?

- phi

Degree is the biggest exponent
classification is polynomial

- anonymous

so first degree binomial?

- anonymous

is that right?

- phi

\[ 10x^2 +53x+63 \]
what is the biggest exponent (little number in the upper right)

- anonymous

oops, 2nd degree

- anonymous

trinomial

- anonymous

i was looking at the the problem, not the solution for A=(2x + 7)(5x + 9) =10x^2 +53x+63

- phi

yes. all the suffices bi, tri, quad are Latin for 2, 3, 4
It helps to know your Latin
FYI, the expression
(2x + 7)(5x + 9)
even if not multiplied out, is 2nd degree
(or "quadratic" )

- phi

though we could not really call it trinomial if it's not multiplied out.

- anonymous

so what do we call it

- phi

part C is the same answer as the other problem, except use multiply instead of add or subtract.

- phi

You posted the answers: 2nd degree, trinomial

- anonymous

so for part c its (10x^2)(53x)(63) ?

- phi

for part B, you might want to also call it quadratic (just in case that is what they are expecting)
for part C, the idea is
if you multiply two polynomials, the answer will be a polynomial
in part A, you do that, and the answer was a polynomial

- anonymous

do i put that for part c?

- phi

in your own words.

- anonymous

ok thankyou! Can you check my answers from the other question??

- anonymous

Side 1: 3x2 − 4x − 1
Side 2: 4x − x2 + 5
The perimeter of the triangle is 5x3 − 2x2 + 3x − 8.
Part A: What is the total length of the two sides, 1 and 2, of the triangle? (4 points)
Part B: What is the length of the third side of the triangle? (4 points)
Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (2 points)
Part A: The total length is 3x^2-x^2,which makes 2x^2+4
Part B: 4-12=-8
Part C:Part a and b both started with polynomials, and had a polynomial as an answer. So its showing that polynomials are closed under subtraction/addition.

- phi

Part A you say
***The total length is 3x^2-x^2***
that leaves out quite a bit.
if you add two polynomials, you have to put in the entire polynomial , not just the cute terms you like

- phi

3x2 − 4x − 1
+
4x − x2 + 5

- anonymous

so do i say "3x2 − 4x − 1+4x − x2 + 5=3x^2-x^2" ??

- phi

the left side is good. the right side should be the "simplified" version
for example you have 3 x^2 terms take away 1 x^2 term
I would combine those to get just 2x^2 (not "3x^2-x^2" because that is not simplified)
then do -4x + 4x (easy I hope?!)
then do -1+5

- anonymous

2x2+4

- phi

yes. You had the correct answer, but how you got the answer looked dubious.

- anonymous

ooh okay

- phi

Part B
I thought we did this. perimeter - (two sides) = 3rd side
you should be showing polynomial (perimeter) - polynomial (from part A) = polynomial (answer)

- phi

You got the answer in the other post.

- anonymous

ill look back at it brb

- anonymous

3x2−4x−1+4x−x2+5=2x^2+4 ?

- anonymous

@phi

- anonymous

no wait thats A 5x3−4x2+3x−12 ?

- phi

first write down the polynomial for the perimeter
then minus sign
then (in parens) the polynomial from part A

- phi

then =
and finally the answer 5x3−4x2+3x−12

- anonymous

5x3 − 2x2 + 3x − 8-(2x^2+4)= 5x3−4x2+3x−12?

- phi

yes

- anonymous

yaay thanks

- phi

part C is ok

- phi

good job. But if concentrate , it would go faster. We had to do that question twice.

- anonymous

okay thankyou

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