When f(x) = $x^{4}$ -2 $x^{3}$ +3 $x^{2}$ -ax+b is divided by x+1 and x-1, we get remainders 19 and 5 respectively. Find the remainder when f(x) is divided by x-3.

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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If f(x)=x4−2x3+3x2−ax+b is a polynomial such that when it is divided by (x−1) and (x+1), then the remainders are 5 and 19 respectively. If f(x) is divided by (x−2), then the remainder is:

The correct option is D 10P(1)=5⟹2−a+b=5⟹b−a=5.........(i)P(−1)=6+a+b=19⟹b+a=13....(ii)Solving (i) and (ii), we getb=8,a=5Hence, remainder =P(2)=10.

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 $19$ respectively. If $f (x)$ is divided by $(x - 2)$ , then the remainder is:

The correct option is D $10$
$P (1) = 5 ⟹ 2 - a + b = 5 ⟹ b - a = 5$ .........(i)
$P (- 1) = 6 + a + b = 19 ⟹ b + a = 13$ ....(ii)
Solving (i) and (ii), we get
$b = 8, a = 5$
Hence, remainder $= P (2) = 10$ .