Question

Divide -3x3 - 2x2 - x - 2 by x – 2.

Answer 1

A. -3x2 + 4x + 15
B. -3x2 + 4x + 15, R 32
C. -3x2 - 8x - 17
D. -3x2 - 8x - 17, R –36

Answer 2

@neer2890

Answer 3

you want shortcut or a proper method...?

Answer 4

the easiest way to understand lol

Answer 5

are you still there

Answer 6

One method is to use remainder theorem:

It says that the remainder obtained on dividing some polynomial P (x) by (x-a) is P(a) i.e. in polynomial P(x) put a in place of x and then solve it.

Answer 7

For example, here in this case:

P(x) = -3x^3 - 2x^2 - x - 2

we are dividing it by (x-2) , so, the remainder would be:

P(2)

Now, P(2) = -3*(2)^3 - 2(2)^2 - 2 -2

Answer 8

Can you solve P(2) ?

Answer 9

-36

Answer 10

Good

See:

\[\large{P(2) = -3*(2)^3 - 2(2)^2 - 2 - 2}\]
\[\large{\implies P(2) = -3*8 - 2*4 - 2 - 2}\]
\[\large{\implies P(2) = -24 - 8 - 2 - 2}\]
\[\large{\implies P(2) = -36}\]

Answer 11

So, remainder = -36

Answer 12

Now, if there would have been more than 1 option with remainder -36 , then, we would have applied division theorem:

\[\large{\text{Dividend} = \text{Quotient}\times \text{Divisor} + \text{Remainder}}\]

Answer 13

Now, you have :

\[\large{\text{Dividend} = -3x^3 -2x^2 - x -2}\]

\[\large{\text{Divisor} = x-2}\]

\[\large{\text{Remainder} = -36}\]

\[\large{\text{Quotient} = ?}\]

Answer 14

So, can you calculate the quotient ?

Answer 15

i don't know how to do that

Answer 16

All right lets see:

\[\large{\text{Dividend} = \text{Divisor}\times \text{Quotient} + \text{Remainder}}\]
\[\large{\implies\text{Dividend} - \text{Remainder} = \text{Divisor}\times \text{Quotient}}\]
\[\large{\implies \text{Quotient} = \cfrac{\text{Dividend}-\text{Remainder}}{\text{Divisor}}}\]

Answer 17

Now, I am going to put the values

Answer 18

\[\large{\implies \text{Quotient} = \cfrac{(-3x^3 -2x^2 -x - 2) - (-36)}{(x-2)}}\]

\[\large{\implies \text{Quotient} = \cfrac{-3x^3 - 2x^2 - x - 2 + 36}{x-2}}\]

\[\large{\implies \text{Quotient} = \cfrac{-3x^3 - 2x^2 - x + 34}{x-2}}\]

Answer 19

Thus,

\[\large{\text{Quotient} = -3x^2 - 8x - 17}\]

Answer 20

Thus, D is the correct option.

Now do you get it ?

Answer 21

ok i see so it is D, thank you so much for helping but i have another question can you help me on that one too