Question

The length of a rectangle is (5x2 + 4x - 4) units, and its width is (4x3 - 2x + 6) units.

Part A: What is the area of the rectangle? Show your work. (5 points)

Part B: Does the answer for Part A show that polynomials are closed under an operation? Justify your answer. (3 points)

Part C: What is the degree and classification of the expression obtained in Part A? (2 points)

Answer 1

@dumbcow ;)

Answer 2

Area = length*width

multiply the polynomials by distributing

Answer 3

combined like terms to get 2x and 2, and I can't combine 5x2 and 4x3. @dumbcow

Answer 4

correct but that is ADDING
for this problem to get area you have to MULTIPLY

Answer 5

so i get -8x and -24?

Answer 6

(5x^2 +4x -4)(4x^3 -2x +6) = (5x^2)(4x^3) + (5x^2)(-2x) + (5x^2)(6) +(4x)(4x^3)+ ...

see the pattern

Answer 7

btw it would be -8x^2

when multiplying polynomials you ADD the EXPONENTS

Answer 8

(5x^2)(4x^3) for that would i do (5x)(4x) etc, like what you said?

Answer 9

not sure what you mean
(5x^2)(4x^3) = 20x^5

Answer 10

Okay, I'm sorry it's late. I should be asleep x( so that makes the answer...?

Answer 11

nope you have to do it...after distributing each term, then you ADD like terms

Answer 12

-10x^2 is the next one?

Answer 13

30x^2 next?

Answer 14

close .... -10x^3

add the exponents( x has exponent of 1)

Answer 15

30x^2 correct

Answer 16

so we have so far20x^5 + -10x^3 + 30x^2

Answer 17

yep now we have to distribute the "4x"
(4x)(4x^3) + (4x)(-2x)+ (4x)(6)

Answer 18

16x^4 + -8x^2 + 24x

Answer 19

correct :)

now distribute the "-4"

Answer 20

What is the equation to do that?

Answer 21

its just multiplying...you are already doing it

(4x)(4x^3) + (4x)(-2x)+ (4x)(6) ---> this was multiplying the "4x" with other polynomial

Answer 22

(-4)(4x^3) + (-4)(-2x)+ (-4)(6) ?

-16x^3 + 8x + -24

Answer 23

yes

now combine like terms

Answer 24

So what is the equation so far so I can combine like terms, i didnt write it out

Answer 25

oh well yeah you need to write them out since there are a lot

--> 20x^5 -10x^3 +30x^2 16x^4 + -8x^2 + 24x -16x^3 +8x -24

Answer 26

so far ive combined two like terms to get 160x^6

Answer 27

-240x^4 is another

Answer 28

careful when ADDING like terms. you also just add the numbers

--> -26x^3

--> 22x^2

Answer 29

I'm confused >_<. so just give me more help with adding these like terms? I tried but i keep getting stuck

Answer 30

ok
-10x^3 -16x^3 = -26x^3 (ADDING)

(-10x^3)(-16x^3) = 160x^6 (MULTIPLYING)

Answer 31

20x^5 -10x^3 +30x^2 16x^4 + -8x^2 + 24x -16x^3 +8x -24

I can't find anymore like terms

Answer 32

find the "x" terms

Answer 33

24x, 8x

Answer 34

good, add those and you are done

Answer 35

I dont have to addthe ones with exponenets?

Answer 36

which ones?

Answer 37

So what is the final answer?

Answer 38

20x^5 + 16x^4 -26x^3 + 22x^2 + 32x -24

Answer 39

Okay, thats what i had just wanted to make sure. also. Part B: Does the answer for Part A show that polynomials are closed under an operation? Justify your answer. having trouble with that

Answer 40

Part B: closed under multiplication

Part C: 5th degree polynomial (degree = highest exponent)

Answer 41

Thank you.

Answer 42

your welcome