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Standard IX

Mathematics

Remainder Theorem

The polynomia...

Question

The polynomial x⁴- 2x³+ 3x²- ax + b when divided by x +1 and x -1 give remainder 19 and 5 respectively . Find the remainder when the polynomial is divided by x -3

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Solution

Dear student solution is correct.
your query is how you get values of a and b so see
We have
a+b=13 ....(1)
-a+b=3. ....(2)
Now from (1)
b=13-a
From (2)
b=3+a
now equating both values of b
13-a=3+a

I hope you get the solution now

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Similar questions

Q. The polynomial

f (x) = x^{4} - 2 x^{3} + 3 x^{2} - a x + b

when divided by

(x - 1)

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respectively . Find the value of

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f (x)

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The polynomial $p (x) = x^{4} - 2 x^{3} + 3 x^{2} - a x + b$ when divided by (x-1) and (x +1) leaves the remainders 5 and 19 respectively. Find the values of a and b. Hence, find the remainder when p(x) is divided by (x -2).

Q. If

f (x) = x^{4} - 2 x^{3} + 3 x^{2} - a x + b

is a polynomial such that when it is divided by

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and

19

. Determine the remainder when

f (x)

is divided by

(x - 2)

Q. If

f (x) = x^{4} - 2 x^{3} + 3 x^{2} - a x + b

is a polynomial such that when it is divided by

(x - 1)

and

(x + 1)

, then the remainders are

5

and

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respectively. If

f (x)

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Q. If

f (x) = x^{4} - 2 x^{3} + 3 x^{2} - a x + b

is a polynomial such that when it is divided by

(x - 1)

and

(x + 1)

, the remainders are

5

and

19

respectively, the remainder when

f (x)

is divisible by

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The polynomial x​​​​​​4 - 2x3 + 3x2 - ax + b when divided by x +1 and x -1 give remainder 19 and 5 respectively . Find the remainder when the polynomial is divided by x -3

Dear student solution is correct. your query is how you get values of a and b so see We have a+b=13 ....(1) -a+b=3. ....(2) Now from (1) b=13-a From (2) b=3+a now equating both values of b 13-a=3+a I hope you get the solution now

The polynomial x⁴- 2x³+ 3x²- ax + b when divided by x +1 and x -1 give remainder 19 and 5 respectively . Find the remainder when the polynomial is divided by x -3

Dear student solution is correct.
your query is how you get values of a and b so see
We have
a+b=13 ....(1)
-a+b=3. ....(2)
Now from (1)
b=13-a
From (2)
b=3+a
now equating both values of b
13-a=3+a

I hope you get the solution now