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
Identify polynomials in the following:
`f(x)=2+3/x+4x`
If `f(x) = 2x^2 - 13x^2 + 17x + 12` find f(2)
f(x) = x4 − 3x2 + 4, g(x) = x − 2
In each of the following, use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not: (1−7)
f(x) = x3 − 6x2 + 11x − 6; g(x) = x − 3
f(x) = 3x4 + 17x3 + 9x2 − 7x − 10; g(x) = x + 5
f(x) = x3 − 6x2 + 11x − 6, g(x) = x2 − 3x + 2
x3 − 10x2 − 53x − 42
If f(x) = x4 − 2x3 + 3x2 − ax − b when divided by x − 1, the remainder is 6, then find the value of a + b
One factor of x4 + x2 − 20 is x2 + 5. The other factor is
Factorise the following:
(a + b)2 + 9(a + b) + 18
