Question

Check my answer please?
Divide -3x^3-4x^2+4x+3 by x-2
My answer: -3x^2+2x+24

Answer 1

Check your answers yourself by multiplication:

\[(-3x^2+2x+24)(x-2) = -3x^3 + 6x^2 + 2x^2 - 4x + 24x - 48\]\[ = -3x^3 + 8x^2 + 20x - 48\] which is not what you started with, so you've made a mistake somewhere. Is this division supposed to come out even, without a remainder? If so, it looks like you might have copied the problem incorrectly...

Answer 2

You think you could help me please? I'm not very good at math.

Answer 3

Sure. The most important step is to make sure you're working on the correct problem :-) Can you check that you've copied it correctly?

Answer 4

Yes, it says divide -3x^3 - 4x^2 + 4x + 3 by x -2.

Answer 5

Are you expecting answers may have remainders?

Answer 6

Yes some answers do have remainders.

Answer 7

Okay. This is one of them :-)

Answer 8

How are you doing polynomial division?

Answer 9

By long division.

Answer 10

Okay, so what is the first term of the quotient going to be?

Answer 11

x -2?

Answer 12

No, that's the divisor. What is the biggest power of x you can multiply (x-2) by and subtract from -3x^3 - 4x^2 + 4x + 3?

Answer 13

Oh sorry, um x? Or is it x^2?

Answer 14

just a sec...

Answer 15

okay, \(x^2\) is going to be the highest power of x you can multiply by \((x-2)\). What will the coefficient be? We want to make the \(-3x^3\) term disappear.

Answer 16

3x^3? You add it to -3x^3 right?

Answer 17

You got this correct in your first answer...first term is \(-3x^2\)

When we multiply \((-3x^2)(x-2)\) we get \(-3x^3+6x^2\). Now we subtract that from our original dividend to see what we have left to divide:
\[-3x^3 - 4x^2 + 4x + 3\]\[-3x^3+6x^2\]
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\[0x^3 -10x^2 + 4x + 3\]

Now we repeat the process. We need the \(-10x^2\) term to go away this time, so we multiply by \(-10x\)

Answer 18

\[(-10x)(x-2) = -10x^2+20x\]

\[-10x^2 + 4x + 3\]\[-10x^2+20x\]
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\[0x^2 - 16x + 3\]

Can you do the final step?

Answer 19

I just confused myself. Math is such a drag.

Answer 20

Did you finally get the right answer, or do I have some more explaining to do?