Question

When $x^{3}-2x^{2}+ax-b$ is divided by $x^2-2x-3$, the remainder is x-6 .The values of a and b are respectively.​

Answer 1

Answer:

ANSWER

x 3−2x 2+ax−b is divided by x 2−2x−3

and the remainder obtained is x−6.

Now, the first term in the quotient will be x since the coefficient of x 3 is 1.

So, x(x 2x−3)=x

3−2x 2 −3x, which when subtracted from the dividend gives (a+3)x−b

Since the degree of the above term is less than the divisor, it is the remainder and so we equate it to x−6

Hence, a+3=1 and b=6

⇒a=−2,b=6

Step-by-step explanation:

Hope it helps you

Answer 2

Answer:

ANSWER

x

3

−2x

2

+ax−b is divided by x

2

−2x−3 and the remainder obtained is x−6.

Now, the first term in the quotient will be x since the coefficient of x

3

is 1.

So, x(x

2

−2x−3)=x

3

−2x

2

−3x, which when subtracted from the dividend gives (a+3)x−b

Since the degree of the above term is less than the divisor, it is the remainder and so we equate it to x−6

Hence, a+3=1 and b=6

⇒a=−2,b=6

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