Question

If f(x) = 2x^4-2x^3+3x^2-ax+b is a polynomial such that when it is divided
by (x-1) and (x+1) the remainders are respectively 7 and 19.
Determine the value of a and b.​

Answer 1

Answer:

a = 4 and b = 8

Step-by-step explanation:

Given that

f(x) = 2x⁴-2x³+3x²-ax+b

f(1) = 7 ----- (1)

f(-1) = 19 ------(2)

From (1):

f(1) = 2 - 2 + 3 - a + b = 7

=) - ( a - b ) = 4

a - b = -4 ----- (3)

From (2):

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

=) a + b = 12 -------- (4)

From (3) and (4):

(3)

a - b = -4

-b = -4 - a

b = 4 + a

(4)

a + b = 12

a + a + 4 = 12

2a = 8

a = 4

(4)

a + b = 12

4 + b = 12

b = 8

hope it helps you..

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