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:

Step-by-step explanation:

(3x² + 3x + x + 1 )/ 1

= (3x² + 3x + x + 1 )

= 3x ( x + 1 ) + 1 ( x + 1  )

= ( 3x + 1 ) ( x + 1 )

the factors are  ( 3x + 1 ) ( x + 1 )

the answer is (i)

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

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.