Question

Find the remainder when x + 3x2 + 3x + 1 is divided by
1
(i) x + 1
(ii) x- 1/2
(iii) x ​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Given:

Find the remainder when x³ + 3x² + 3x + 1 is divided by —

(i) x + 1 (ii) x-1/2 (iii) x

1st solution:- The divisor here is x + 1 = x-(-1)

So, by remainder theorem, when p(x) is divided by x+1, the remainder is p(-1)

➠p(x) = x³ + 3x² + 3x + 1

➠ p(-1) = (-1)³ + 3(-1)² + 3(-1) + 1

= -1 + 3 - 3 + 1

= 0

Hence, the required remainder is 0.

2nd Solution:- The divisor here is x-½ [From x - a with a = ½

So, by remainder theorem, when p(x) is divided by x-½, the remainder is p(½).

➠ p(x) = x³ + 3x² + 3x + 1

➠ p(½) = (½)³+ 3(½) + 3(½) + 1

= ⅛ + ¾ + ³/² + 1

= 27/8

Hence, the required remainder is 27/8.