Question

Question 2.
Find the remainder when polynomial p(x) = 2% + 2.c - 3 is divided by x + 1​

Answer 1

Answer:

p(x) = x4 - 3x2 + 2x - 5

According to remainder theorem, the required remainder will be = p(2)

p(x) = x4 - 3x2 + 2x - 5

∴ p(2) = 24 - 3(2)2 + 2(2) - 5

=16 - 12 + 4 - 5 = 3

Answer 2

Answer:

x

2

−1→(x+1)(x−1)

x

2

−1[P(x)][Q(x)]→R=ax+b

⇒(x+1)(x−1)⋅xQ(x)+ax+b=P(x)

whenx=−1→1=−a+b

whenx=1→2=a+b

solving the above equations we get, a=

2

1

,b=

2

3

Remainder =ax+b⇒

2

1

x+

2

3

=

2

1

(x+3)