Advertisements
Advertisements
Question
If x3 + 6x2 + kx + 6 is exactly divisible by (x + 2), then k = ?
Options
−6
−7
−8
11
Advertisements
Solution
11
Explanation;
Hint:
p(x) = x3 + 6x2 + kx + 6
Given p(−2) = 0
(−2)3 + 6(−2)2 + k(−2) + 6 = 0
−8 + 24 – 2k + 6 = 0
22 – 2k = 0
k = `22/2`
= 11
APPEARS IN
RELATED QUESTIONS
Find 'a' if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
Find the value of a, if the division of ax3 + 9x2 + 4x – 10 by x + 3 leaves a remainder 5.
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(x2 − 7x + 9) ; (x + 1)
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(2x3 − 2x2 + ax − a) ; (x − a)
What number should be added to polynomial f(x)= 12x3 + 16x2 - 5x - 8 so that the resulting polynomial is exactly divisible by (2x - 1) ?
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x - 4
Using remainder theorem, find the value of a if the division of x3 + 5x2 – ax + 6 by (x – 1) leaves the remainder 2a.
Find ‘a’ if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
A polynomial in ‘x’ is divided by (x – a) and for (x – a) to be a factor of this polynomial, the remainder should be ______.
4x2 – kx + 5 leaves a remainder 2 when divided by x – 1. The value of k is ______.
