Question

If x^103 - x^102 + x^97 + 2x + 7 is divided by (x^3 - x) then find the remainder​

Answer 1

Answer:

Remainder= 10 and 2

Step-by-step explanation:

p(x)=x^103-x^102+x^97+2x+7

g(x)=x^3-x

0=x(x^2-1)

0=x^2-1

x=±1

p(+1)= 1^103- 1^102+ 1^97+ 2*1 +7       or     p(-1)= (-1)^103- (-1)^102+ (-1)^97+ 2*-1 +7

      = 1-1+1+2+7                                                  = -1 -1 -1 -2 + 7

      = 10                                                             = -5+7  = +2

Answer 2

Answer:

Remainder = 10 or 2

Step-by-step explanation:

p(x) = x¹⁰³ - x¹⁰² + x⁹⁷ + 2x + 7

g(x) = x³ - x

   0 = x(x² - 1)

   0 = x² - 1

   x = ±1

p(+1) = 1¹⁰³ - 1¹⁰² + 1⁹⁷ + 2×1 +7   or     p(-1) = (-1)¹⁰³ - (-1)¹⁰² + (-1)⁹⁷ + 2×(-1) + 7

      = 1-1+1+2+7                                      = -1 -1 -1 -2 + 7

      = 10                                                 = -5+7  = 2