CBSE Class 9 Answered

When f(x) is divided by (x-1), it leaves a remainder 5

f(1) = 5

 1 - 2(1)³ + 3(1)² - a(1) + b = 5

 1 - 2 + 3 - a +b = 5

 -a + b = 3 … (i)

When f(x) is divided by (x+1), it leaves a remainder 19

f(-1) = 19

 (-1)⁴ - 2(-1)³ + 3(-1)² - a(-1) + b = 19

1 + 2 + 3 + a + b = 19

a +b = 13 … (ii)

Adding (i) and (ii),

2b = 16  _{b = 8}

_{(i)  a = b - 3 = 8 - 3 = 5}

Therefore,  f(x) = x⁴ - 2x³ + 3x² - 5x + 8 

When f(x) is divided by x - 3, the remainder will be

f(3) = 3⁴ - 2(3)³ + 3(3)² - 5(3) + 8 = 81 + 9 - 15 + 8 = 83