AP ICET 2019 Shift 2 Paper

Question : 124 of 200

Marks: +1, -0

A polynomial Φ (x) leaves remainders -1 and 3 when divided by x-3 and x+1 respectively. Then the remainder, when that polynomial Φ (x) is divided by

x^2-2x-3

Solution:

Let the required remainder be ax + b and quotient be q(x)

∴\∅(x)=(x-3)(x+1) q(x)+a x+b

\∅(3)=3 a+b ⇒ 3 a+b=-1

→ (1)

\∅(-1)=-a+b ⇒-a+b=3

→ (2)
Solving (1) & (2),

= a = –1, b = 2

∴ Required remainder

2-x

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