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.
RELATED QUESTIONS
Find ‘a‘ if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leave the same remainder when divided by x + 3.
The polynomials ax3 + 3x2 – 3 and 2x3 – 5x + a, when divided by x – 4, leave the same remainder in each case. Find the value of a.
When divided by x – 3 the polynomials x3 – px2 + x + 6 and 2x3 – x2 – (p + 3) x – 6 leave the same remainder. Find the value of ‘p’.
Find without division, the remainder in the following:
8x2 - 2x + 1 is divided by (2x+ 1)
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.
(x – 2) is a factor of the expression x3 + ax2 + bx + 6. When this expression is divided by (x – 3), it leaves the remainder 3. Find the values of a and b.
If x + 1 is a factor of 3x3 + kx2 + 7x + 4, then the value of k is
By remainder theorem, find the remainder when, p(x) is divided by g(x) where, p(x) = 4x3 – 12x2 + 14x – 3; g(x) = 2x – 1
Determine which of the following polynomials has x – 2 a factor:
4x2 + x – 2
The polynomial p(x) = x4 – 2x3 + 3x2 – ax + 3a – 7 when divided by x + 1 leaves the remainder 19. Find the values of a. Also find the remainder when p(x) is divided by x + 2.
