Use factor theorem to find whether polynomial g(x) is a factor of poly

1.	Use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not:f(x) = x5 + 3x4 – x3 – 3x2 + 5x + 15, g(x) = x + 3
Answer» If g(x) is a factor of f(x), then the remainder will be zero that is g(x) = 0. g(x) = x + 3 = 0, then x = -3 Remainder = f(-3) Now, f(-3) = (-3)⁵ + 3(-3)⁴ – (-3)³ – 3(-3)² + 5(-3) + 15 = -243 + 3 x 81 -(-27)-3 x 9 + 5(-3) + 15 = -243 + 243 + 27 - 27 - 15 + 15 = 0 Therefore, g(x) is a factor of f(x).

Use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not:f(x) = x5 + 3x4 – x3 – 3x2 + 5x + 15, g(x) = x + 3

Answer»

If g(x) is a factor of f(x), then the remainder will be zero that is g(x) = 0.

g(x) = x + 3 = 0, then x = -3

Remainder = f(-3)

Now,

f(-3) = (-3)⁵ + 3(-3)⁴ – (-3)³ – 3(-3)² + 5(-3) + 15

= -243 + 3 x 81 -(-27)-3 x 9 + 5(-3) + 15

= -243 + 243 + 27 - 27 - 15 + 15

= 0

Therefore, g(x) is a factor of f(x).