Question

EXERCISE 2.3
Find the remainder when x + 3x² + 3x + 1 is divided by
1
(i) x + 1
(ii) X -
(iii) x
​

Answer 1

1) by x+1 : divisor

x+1 = 0 => x = -1

let p(x) = x^3+3x^2+3x+1

put x = -1

p(1) = (-1)^3+3(-1)^2+3(-1)+1

= -1+3-3+1=0

2) by x-1/2 : divisor

x-12 = 0 => x = 1/2

p(x) = x^3+3x^2+3x+1

put x = 1/2

p(1/2) = (1/2)^3+3(1/2)^2+3(1/2)+1

= 1/8+3(1/4)+3/2+1

= 1/8+3/4+3/2+1

= 1+3(2)+3(4)+1(8)/8

= 1+6+12+8/8

= 27/8

3) by x

x = 0

p(x) = (0)^3+3(0)^2+3(0)+1

= 1