Advertisements
Advertisements
Question
Determine the following polynomial has (x + 1) a factor:
x3 + x2 + x + 1
Advertisements
Solution
If (x + 1) is a factor of p(x) = x3 + x2 + x + 1, then p (−1) must be zero, otherwise (x + 1) is not a factor of p(x).
p(x) = x3 + x2 + x + 1
p(−1) = (−1)3 + (−1)2 + (−1) + 1
= − 1 + 1 − 1 + 1
= 0
Hence, x + 1 is a factor of this polynomial.
APPEARS IN
RELATED QUESTIONS
Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:
p(x) = 2x3 + x2 – 2x – 1, g(x) = x + 1
Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:
p(x) = x3 + 3x2 + 3x + 1, g(x) = x + 2
Find the value of k, if x – 1 is a factor of p(x) in the following case:
p(x) = x2 + x + k
Find the value of k, if x – 1 is a factor of p(x) in the following case:
p(x) = `2x^2+kx+sqrt2`
Find the value of k, if x – 1 is a factor of p(x) in the following case:
p(x) = kx2 – 3x + k
Factorise:
2y3 + y2 – 2y – 1
Find the factor of the polynomial given below.
3y2 – 2y – 1
If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is ______.
Show that 2x – 3 is a factor of x + 2x3 – 9x2 + 12.
Factorise the following:
9x2 – 12x + 3
