Question

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.

• A. 47
• B. 48
• C. 49
• D. 46

Answer 1

The correct option is A

47

f(-1) = 19

${(-1)}^4$ -2 ${(-1)}^3$ + 3 ${(-1)}^2$ – a (-1) + b = 19

1 + 2 + 3 + a + b = 19

a + b = 13 ---- (1)

f(1) = 5

${\left(1\right)}^4$ -2 ${\left(1\right)}^3$ + 3 ${\left(1\right)}^2$ – a (1) + b = 5

1 – 2 + 3 – a + b = 5

-a + b = 3 ----- (2)

On solving (1) and (2), we get

a = 5, b = 8

f(x ) = $x^4$ - 2$x^3$ +3$x^2$ - 5x+8

f(3) = 47