Advertisements
Advertisements
प्रश्न
Determine the following polynomial has (x + 1) a factor:
x4 + x3 + x2 + x + 1
Advertisements
उत्तर
If (x + 1) is a factor of p(x) = x4 + x3 + x2 + x + 1, then p (−1) must be zero, as a result (x + 1) is not a factor of p(x).
p(x) = x4 + x3 + x2 + x + 1
p(−1) = (−1)4 + (−1)3 + (−1)2 + (−1) + 1
= 1 − 1 + 1 − 1 + 1
= 1
As p(−1) ≠ 0,
Therefore, x + 1 is not a factor of this polynomial.
APPEARS IN
संबंधित प्रश्न
Determine the following polynomial has (x + 1) a factor:
x3 + x2 + 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) = kx2 – 3x + k
One of the factors of (25x2 – 1) + (1 + 5x)2 is ______.
The factorisation of 4x2 + 8x + 3 is ______.
Show that 2x – 3 is a factor of x + 2x3 – 9x2 + 12.
Find the value of m so that 2x – 1 be a factor of 8x4 + 4x3 – 16x2 + 10x + m.
Factorise the following:
1 – 64a3 – 12a + 48a2
Factorise:
`2sqrt(2)a^3 + 8b^3 - 27c^3 + 18sqrt(2)abc`
