Question

CAN YOU PLEASE HELP?


The length of a rectangle is (6x2 + 3x - 2) units, and its width is (x3 - 2x + 5) 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

Area = length * width = (6x^2 + 3x - 2) * (x^3 - 2x + 5)

Multiply it out and simplify.

Answer 2

is that for part a?

Answer 3

Yes. Take the first term 6x^2 and multiply each of the term x^3, -2x & 5. Then take 3x and multiply each of the term x^3, -2x & 5. Do the same with -2.
Then add like terms and simplify.

Answer 4

What is 6x^2 * x^3 ?

Answer 5

6x5?

Answer 6

Yes. 6x^5. Now do the same with the rest of the terms. Distribute the terms.

Answer 7

(6x^2 + 3x - 2) * (x^3 - 2x + 5) =
6x^2 * x^3 + 6x^2 * (-2x) + 6x^2 * 5 + 3x * x^3 + 3x * (-2x) + 3x * 5 - 2 * x^3 - 2 * (-2x) - 2 * 5 = ?

Answer 8

(6x2+3x−2)(x3−2x+5)?

Answer 9

wait that's wrong..

Answer 10

That is what we started with. We need to multiply those two expressions. So you need to distribute them. And I have shown in my previous reply how to distribute them.

Answer 11

when multiplying i got 6x5+3x4−14x3+24x2+19x−10

Answer 12

Good job!!!

Answer 13

thanks!. could you please help with part b and c?

Answer 14

Part b) In part a) we multiplied two polynomials with integer coefficients and the results was 6x^5+3x^4−14x^3+24x^2+19x−10 which is also a polynomial with integer coefficients. Therefore, the multiplication of two polynomials results in a polynomial and therefore polynomials are closed under multiplication.

Answer 15

thanks your a saint

Answer 16

also if you could lead me to the right direction on point c?

Answer 17

part c) The degree of a polynomial is the highest degree of its variable. The degree of the result obtained in part a is five. This is a fifth degree polynomial. Sometimes it is also called a quintic polynomial (meaning fifth degree).

Answer 18

thanks !!!!!! so much i really appreciate it

Answer 19

I don't really understand part c.