FUNCTIONS 9

If f(x) = x⁴ + ex² + 3x + 5 has a remainder of 22 when divided by x+2; find e.

solution

f(x) = x⁴ + ex² + 3x + 5

x + 2 = 0

x = -2

f(x) = (-2)⁴ + e(-2)² + 3(-2) + 5 = 22

So, (-2)⁴ + e(-2)² + 3(-2) + 5 = 22

16 + 4e + (-6) + 5 = 22

4e + 16 + (-6) + 5 = 22

4e + 15 = 22

4e = 22 - 15

4e = 7

4e = 7

4      4

e = ⁷/4

hence e= ⁷/4

TRY THIS......................

If f(x) = x⁴ - wx² + 6x - 2 has a remainder of 20 when divided by x+3; find w.