Find the remainder when the polynomial f(x) = 2x4 - 2x2 - x + 2 is d

1.	Find the remainder when the polynomial f(x) = 2x4 - 2x2 - x + 2 is divided by x + 2.
Answer» If x + 2 = 0 x = -2 f(x) = 2x⁴ – 6x³ + 2x² – x + 2, [By remainder theorem] f(x) = 2(-2)⁴ – 6(-2)³ + 2(- 2)² – (- 2) + 2 = 2(16) – 6(- 8) + 2(4) + 2 + 2 = 32 + 48 + 8 + 2 + 2 = 92 Hence, required remainder = 92. Given , Polynomial f(x) = 2x⁴ - 2x² - x + 2 g (x) = x + 2 = 0 x = -2 Putting value of x in equation , f(-2) = 2x4 – 6x3 + 2x2 – x + 2, f(-2) = 2(-2)4 – 6(-2)3 + 2(- 2)2 – (- 2) + 2 = 2(16) – 6(- 8) + 2(4) + 2 + 2 = 32 + 48 + 8 + 2 + 2 = 92 Hence, remainder = 92

Find the remainder when the polynomial f(x) = 2x4 - 2x2 - x + 2 is divided by x + 2.

Answer»

If x + 2 = 0

x = -2

f(x) = 2x⁴ – 6x³ + 2x² – x + 2, [By remainder theorem]

f(x) = 2(-2)⁴ – 6(-2)³ + 2(- 2)² – (- 2) + 2

= 2(16) – 6(- 8) + 2(4) + 2 + 2

= 32 + 48 + 8 + 2 + 2

= 92

Hence, required remainder = 92.

Given , Polynomial f(x) = 2x⁴ - 2x² - x + 2

g (x) = x + 2 = 0 x = -2

Putting value of x in equation ,

f(-2) = 2x4 – 6x3 + 2x2 – x + 2,

f(-2) = 2(-2)4 – 6(-2)3 + 2(- 2)2 – (- 2) + 2

= 2(16) – 6(- 8) + 2(4) + 2 + 2

= 32 + 48 + 8 + 2 + 2 = 92

Hence, remainder = 92