Advertisements
Advertisements
Question
(x+1) is a factor of xn + 1 only if
Options
n is an odd integer
n is an even integer
n is a negative integer
n is a positive integer
Advertisements
Solution
The linear polynomial (x - 1)is a factor of `x^n + 1,`only if `f(-1) = (-1)^n + 1 = 0`
If n is odd integer, then `f(-1) = -1 + 1 = 0`
APPEARS IN
RELATED QUESTIONS
Write the degrees of the following polynomials:
7
If f(x) = 2x2 - 13x2 + 17x + 12 find f(-3).
Find the remainder when x3 + 3x2 + 3x + 1 is divided by \[x - \frac{1}{2}\].
f(x) = 3x3 + x2 − 20x +12, g(x) = 3x − 2
In the following two polynomials, find the value of a, if x + a is a factor x3 + ax2 − 2x +a + 4.
y3 − 2y2 − 29y − 42
If x51 + 51 is divided by x + 1, the remainder is
If x2 + x + 1 is a factor of the polynomial 3x3 + 8x2 + 8x + 3 + 5k, then the value of k is
Factorise the following:
`sqrt(5)"a"^2 + 2"a" - 3sqrt(5)`
Which of the following has x – 1 as a factor?
