Question

find the remainder when the polynomial p(x)=x4+2x3-3x2+x-1 is divided by g(x)=x-2

class 9 CBSE ​

Answer 1

Answer:

Remainder = 21

Step-by-step explanation:

Given:

• p(x) = x⁴ + 2x³ - 3x² + x - 1
• g(x) = x - 2

To find:

Remainder = ?

Solution:

In this question, p(x) is divided by g(x). So, equate g(x) to 0. You will obtain the value of x. Substitute this value of x in p(x) equation and you will get the remainder. This procedure is known as the 'Remainder theorem'

g(x) = x - 2 = 0

⇒ x - 2 = 0

⇒ x = 2

Put this value of x in p(x) Equation.

p(x) = x⁴ + 2x³ - 3x² + x - 1

p(2) = (2)⁴ + 2(2)³ - 3(2)² + 2 - 1

⇒ p(2) = 16 + 16 - 3(4) + 2 - 1

⇒ p(2) = 32 - 12 + 2 - 1

⇒ p(2) = 21

∴ The remainder when p(x) is divided by g(x) = 21