Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
If g(x) = x + 2 is a factor of the given polynomial p(x), then p(−2) must be 0.
p(x) = x3 + 3x2 + 3x + 1
p(−2) = (−2)3 + 3(−2)2 + 3(−2) + 1
= − 8 + 12 − 6 + 1
= −1
As p(−2) ≠ 0,
Hence, g(x) = x + 2 is not a factor of the given polynomial.
APPEARS IN
संबंधित प्रश्न
Determine the following polynomial has (x + 1) a factor:
x3 + x2 + x + 1
Find the value of k, if x – 1 is a factor of p(x) in the following case:
p(x) = x2 + x + k
Factorise:
x3 – 2x2 – x + 2
Factorize the following polynomial.
(x2 – 2x + 3) (x2 – 2x + 5) – 35
Show that x + 3 is a factor of 69 + 11x – x2 + x3.
Determine which of the following polynomials has x – 2 a factor:
3x2 + 6x – 24
Factorise:
6x2 + 7x – 3
Factorise the following:
9x2 – 12x + 3
Factorise the following:
1 – 64a3 – 12a + 48a2
Factorise the following:
`8p^3 + 12/5 p^2 + 6/25 p + 1/125`
