Can you help me with this mathematics question?

Question

it's about simplifying an expression.

the expression is

x^3 + 9x^2 + 14x
-----------------------
x^2 - 4

this is what i got:

(x^2 + 2x) (x + 7)
-----------------------
(x - 2)^2

did i do it right?

Answer 1

No.

Factor x out of the numerator leaving x*(x^2 + 9x + 14)

This factors to x*(x+7)*(x+2)

The denominator is the difference of two squares:

x^2 - 4 = (x+2)*(x-2)

Therefore you're left with:

[x*(x+7)*(x+2)] / [(x+2)*(x-2)]

Which simplifies to:

[x*(x+7)] / (x-2)

Answer 2

x^2 - 4 = (x-2)(x+2) (You can see that (x-2)^2 = x^2 -4x + 4 if you just do it all out.) So that's the denominator.

Now in your numerator, you can factor out an x first to make it easier to work with, so you've got x*(x^2 + 9x + 14) =
= x (x+7)(x+2).

So in total you would have
x(x+7)(x+2)
--------------
(x-2)(x+2)

Which is the same as
x(x+7)
--------
(x-2)

SO LONG AS YOU KNOW THAT X is not equal to 2 or -2 (otherwise you are dividing by zero).

You can check your numerator just as you can check your denominator and in this case you see you have the same thing. So just multiply out what you've got.
(x^2 + 2x) (x + 7) = x^3 + 2x^2 + 7x^2 + 14x, which is exactly what you wanted, only it's not actually "simplified," since you can pull out an x. So your answer was very close.

Answer 3

1. (x^3+9x^2+14x)/(x^2 - 4)

First: factor the numerator - find the least common factor.

x(x^2+9x+14)

now, you have... [x(x^2+9x+14)]/(x^2 - 4)

SEc: factor the numerator - multiply the 1st & 3rd term to get 14. find two numbers that give you 14 when multiplied & 9 (2nd term) when added/subtracted. the numbers are (2 & 7). rewrite the numerator with the new middle terms.

x^2 + 2x + 7x + 14

*group "like" terms & factor both sets of parenthesis.

(x^2 + 2x) + (7x + 14)
x(x + 2) + 7(x + 2)
(x+2)(x+7)

now, you have... [x(x+2)(x+7)]/(x^2 - 4)

Third: factor the denominator - difference of squares.

[x(x+2)(x+7)]/[(x+2)(x-2)]

now, cross cancel "like" terms...

[x(x+7)]/(x-2)

Answer 4

Write the expression as:

x(x^2 + 9x + 14)/(x^2 - 4)
= [x(x + 7)(x + 2)]/(x + 2)(x - 2)
= x(x + 7)/x - 2
= (x^2 + 7x)/x - 2

Answer 5

this is just the first step in simplifying this expression and it is not quite correct.

first of all (x^2 - 4) is not the difference of squares. it would be simplified to (x -2)(x+2)

second you need to factor an x out of the first term on the top so the expression looks like this:
x (x+2)(x+7)
----------------
(x+2)(x-2)

then you can cancel the (x+2) terms and you're left with:
x (x+7)
---------
x-2

or

x^2 +7
---------
x-2

Answer 6

x square - 4=(x+2)(x-2).it's not (x-2)square.

Answer 7

sorry but i think you're wrong
the first step would be:
x(x^2+9x+14)
------------
(x+2)(x-2)

then it would be:
x(x+7)(x+2)
--------
(x+2)(x-2)

last step is:
x(x+7)
-----
x-2

Answer 8

looks good to me