Find the remainder when x3+3x2+3x+1is divide by 1 x 2. x+π 3. 5+2x

Asked by ashakhushi7 | 29th Jun, 2020, 11:53: AM

Expert Answer:

Given polynomial is P(x) = x3+3x2+3x+1
Using Remainder theorem,
When P(x) is divided by x - 2, the remainder would be P(2) 
P(2) = 23 + 3 x 22 + 3 x 2 + 1 = 8 + 12 + 6 + 1 = 27
 
When P(x) is divided by x + 2, the remainder would be P(-2) 
P(-2) = (-2)3 + 3 x (-2)2 + 3 x (-2) + 1 = -8 + 12 - 6 + 1 = -1
 
When P(x) is divided by x + π, the remainder would be P(-π) 
P(-π) = (-π)3 + 3 x (-π)2 + 3 x (-π) + 1 = -π3 + 3π2 - 6π + 1
 
 
When P(x) is divided by 5 + 2x, the remainder would be P(-5/2) 
P(-5/2) = (-5/2)3 + 3 x (-5/2)2 + 3 x (-5/2) + 1 = (-125/8) + (3 x 25)/4 - 15/2 + 1 = (-125+150-120)/8 + 1 = 5/8 + 1 = 13/8 

Answered by Renu Varma | 30th Jun, 2020, 11:29: AM