Advertisements
Advertisements
Question
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x+1.
Advertisements
Solution 1
Let p(x) = x3 + 3x2 + 3x + 1
x+1 = 0 ⇒ x = -1
∴ Remainder = p(-1) = (-1)3 + 3(-1)2 + 3(-1) + 1
= -1 + 3 - 3 + 1
= 0
Therefore, the remainder is 0.
Solution 2
By long division,
Therefore, the remainder is 0.
APPEARS IN
RELATED QUESTIONS
Find the remainder when x3 – ax2 + 6x – a is divided by x – a.
Find the remainder when x4 – 3x2 + 2x + 1 is divided by x – 1.
Find the remainder when x3 + 3x2 – 12x + 4 is divided by x – 2.
Find ‘a‘ if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leave the same remainder when divided by x + 3.
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 − 19x + 6
Using the Remainder Theorem, factorise the expression 3x3 + 10x2 + x – 6. Hence, solve the equation 3x3 + 10x2 + x – 6 = 0
Find without division, the remainder in the following :
x3 + 8x2 + 7x- 11 is divisible by (x+4)
Find the values of a and b when the factors of the polynomial f(x)= ax3 + bx2 + x a are (x+3) and (2x-1). Factorize the polynomial completely.
When x3 – 3x2 + 5x – 7 is divided by x – 2,then the remainder is
When 2x3 – 9x2 + 10x – p is divided by (x + 1), the remainder is – 24.Find the value of p.
