Question

What is the simplified form of x^4 - 81/ x + 3?

Answer 1

Multiply both by the inverse of the denominator (x-3) to get rid of the bottom. That gives you (x-3)(x^4-81) Multiply that out to get x^5-3x^4-81x+243.

Answer 2

is this the right answer?
x^3 + 3x^2 - 9x - 27? @singlesixx

Answer 3

How did you get that?

Answer 4

im not sure

Answer 5

I don't know either. But I'm pretty sure it's not the right answer.

Answer 6

i think its either
x^3 - 3x^2 + 9x - 27
x^3 + 3x^2 + 9x + 27
or
x^3 + 3x^2 - 9x - 27

Answer 7

Well, to divide a fraction, you multiply by the inverse of the denominator, which is what I did.

Answer 8

you can fist use the difference of 2 squares identity:

a^2 - b^2 = ( a - b)(a + b)

so

x^4 - 81 = (x^2 - 9) (x^2 + 9)

and again applying this to first barackets

= (x - 3)(x + 3)(x^2 + 9)

dividing by ( x + 3):

= (x - 3)(x^2 + 9)

now expand this

Answer 9

(x^2 + 9) (x^2 - 9) --- thses are the answer choices. Okay, lets get to solving this problem.

Answer 10

Okay, I have no idea where that's coming from, so I'm going to go ahead and give up.

Answer 11

x^3 - 3x^2 - 27 but how is there a 9x in the answer choices?

Answer 12

@cwrw238

Answer 13

applying the distributive law:

(x - 3)(x^2 + 9)
= x(x^2 + 9) - 3(x^2 + 9)
= x^3 + 9x -3x^2 - 27
= x^3 -3x^2 + 9x - 27

Answer 14

so basically i had just gave the answer choices which were A - D. I got the answer x^3 - 3x^2 - 27, okay? I don't know how to get the 9x in this answer. Just help me. The closest answer to mine that I got was A, if you look back a little bit above and look at my answer choices. @cwrw238

Answer 15

okay thanks can you help me with just one more problem, please?

Answer 16

ok

Answer 17

Rectangle A has a length of 2x + 6 and a width 0f 3x. Rectangle B has a length of x + 2 and an area of 12 square units greater than Rectangle A's area. What is the simpilifed expression for the width of Rectangle B? @cwrw238

Answer 18

These are the answer choices,
x + 2
x + 1
6x + 6
6(x + 2)(x + 1)

Answer 19

Ahhhh Hellooooo, I need help. @cwrw238

Answer 20

area of rectangle A = length * width = 3x(2x + 6)
area of rectangle B = W(x+2) where W is its width

so as the difference in areas = 12 sq units:-

W(x + 2) - 12 = 3x(2x + 6)

now you need to find W in terms of x

Answer 21

can you do this ?

Answer 22

So, how do you simplify it to the next step?

Answer 23

no not really

Answer 24

thats why i need help.

Answer 25

ok first add 12 to both sides

W(x + 2) = 3x(2x + 6) + 12

now expand RHS

w(x + 2) = 6x^2 + 18x + 12

now take out 6 on RHS:

W(x+ 2) = 3(x^2 + 3x + 2)

next step is to, if possible, factor x^2 + 3x + 2

can u do this?

Answer 26

sorry that should be 6(x^2 + 3x + 2) on the 6th line

Answer 27

an alternative way would be to divide 6x^2 + 18x + 12 by x + 2 using long division

Answer 28

i dont know how to factor 6(x^2 + 3x + 2)

Answer 29

ok maybe you havent done that in your course
have you done long division?

Answer 30

what is long division? this is simplifying rational expressions.

Answer 31

okay so Im thinking the answer is D out of my options look above at my answer choices again. @cwrw238

Answer 32

No the factors of 6(x^2 + 3x + 2) are

6(x + 1)(x + 2)

but but you need to divide this by x + 2