Advertisements
Advertisements
प्रश्न
Determine the following polynomial has (x + 1) a factor:
x3 + x2 + x + 1
उत्तर
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
संबंधित प्रश्न
Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:
p(x) = x3 − 4x2 + x + 6, g(x) = x − 3
Find the factor of the polynomial given below.
`1/2x^2 - 3x + 4`
Factorize the following polynomial.
(y2 + 5y) (y2 + 5y – 2) – 24
Factorize the following polynomial.
(x – 3) (x – 4)2 (x – 5) – 6
If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is ______.
Show that p – 1 is a factor of p10 – 1 and also of p11 – 1.
Factorise:
6x2 + 7x – 3
Factorise:
a3 – 8b3 – 64c3 – 24abc
Factorise:
`2sqrt(2)a^3 + 8b^3 - 27c^3 + 18sqrt(2)abc`
Without finding the cubes, factorise:
(x – 2y)3 + (2y – 3z)3 + (3z – x)3
