Question

Find the quotient of the quantity negative 5 times x to the 3rd power plus 20 times x to the 2nd power minus 25 times x all over negative 5 times x.

−5x3 + 20x2 + 5
x2 − 4x + 5
−x2 − 4x + 5
x2 + 4x − 5

Answer 1

@johnweldon1993

Answer 2

Hey there :)

So we have

\[\large \frac{-5x^3 + 20x^2 - 25x}{-5x}\]

Answer 3

hey. :)

And yeah.

Answer 4

So first...do we notice anything about the numerator?

at first glance, I would see right away that every number is divisible by 5 correct?

Answer 5

correct!

Answer 6

So now let me ask

Is there ANY difference between

\(\large -5x^3 + 20x^2 - 25x\) and \(\large -5(x^3 - 4x^2 + 5x)\)

As you can see, I wrote the 5 on the outside...and if we distribute it back in...we would arrive to the original expression correct?

Answer 7

ya

Answer 8

Okay so now, also notice how every term in the numerator ALSO has an 'x' in it right?

so we can just do the same thing with an 'x' that we did with the '5'

I took the 5 out in front...so now I'm going to put the 'x' out in front

\[\large \frac{-5x(x^2- 4x + 5)}{-5x}\]

still with me? or is that confusing?

Answer 9

um confusing

Answer 10

Alright...so we'll ignore this pat and come back to it :)

So

Lets say we have \[\large 2(3)\]

Well that is 6 right? because we just multiply the 2 into the parenthesis

And if we have

\[\large 2(3x + 1)\]

well of course first we would think to do what is inside the parenthesis first...but we cant do anything here...so all we can do is multiply the 2 into the parenthesis right?

So we multiply BOTH terms by that 2

So this would become 6x + 2 right?

Answer 11

ohh okay yeah

Answer 12

Okay well...

with that same

\[\large (6x + 2)\]

it would make sense...that since each term is divisible by 2...we can "factor" out a 2...which means we divide a 2 out from each term and write it on the outside of parenthesis...

meaning

\[\large 6x + 2\]

would become

\[\large 2(3x + 1)\]

right back where we started....make sense?

Answer 13

okaaaay, yeah make sense for now, lol

Answer 14

Haha for now :P well we'll see how far we can get lol

So back to the beginning

\[\large \frac{-5x^3 + 20x^2 - 25x}{-5x}\]

Remember what we just went over...each number up top is divisible by -5...so we can "factor" it out

\[\large \frac{-5(x^3- 4x^2 + 5x)}{-5x}\]

right? if that doesnt make sense...just see what you would get if you multiplied the -5 back into those parenthesis...you'll be back to where you started right?

Answer 15

yeah.

Answer 16

Good, so if we can do it with the -5...we can do it with the 'x' since each term in the numerator has an 'x'

so if we factor out an 'x' we would have

\[\large \frac{-5x(x^2 -4x + 5)}{-5x}\]

Now to see if you get it any better this time :)

Answer 17

hmm ok

Answer 18

There's only 1 more step so if you still arent comfortable up to here just tell me whats tripping you up :)

Answer 19

i think im understanding it. :P

Answer 20

Lol okay good :P

So wait...smartypants :P what do you think the last step is? just look at what we have...

Answer 21

i dont know. :/

Answer 22

Aww smile :)

Well the last step is to eliminate the -5x

We have a -5x on both the top AND the bottom....and since this is division...they cancel each other out

\[\large \frac{\cancel{-5x}(x^2 - 4x + 5)}{\cancel{-5x}}\]

so all we are left with is...?

Answer 23

with B . :P

Answer 24

Lol perfect :P