Advertisements
Advertisements
Question
Find the number which should be added to x2 + x + 3 so that the resulting polynomial is completely divisible by (x + 3).
Advertisements
Solution
Let the required number be k.
Let f(x) = x2 + x + 3 + k
It is given that f(x) is divisible by (x + 3).
∴ Remainder = 0
f(–3) = 0
(–3)2 + (–3) + 3 + k = 0
9 – 3 + 3 + k = 0
9 + k = 0
k = –9
Thus, the required number is –9.
APPEARS IN
RELATED QUESTIONS
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x.
Find without division, the remainder in the following:
5x3 - 7x2 +3 is divided by (x-1)
Find the value of p if the division of px3 + 9x2 + 4x - 10 by (x + 3) leaves the remainder 5.
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x + 2
Find the remainder (without divisions) on dividing f(x) by x – 2, where f(x) = 2x3 – 7x2 + 3
If (x – 2) is a factor of the expression 2x3 + ax2 + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.
If on dividing 2x3 + 6x2 – (2k – 7)x + 5 by x + 3, the remainder is k – 1 then the value of k is
By remainder theorem, find the remainder when, p(x) is divided by g(x) where, p(x) = x3 – 3x2 + 4x + 50; g(x) = x – 3
By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial: x4 + 1; x – 1
By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x3 – 2x2 – 4x – 1, g(x) = x + 1
