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
Find the value of k, if x – 1 is a factor of p(x) in the following case:
p(x) = x2 + x + k
Factorise:
6x2 + 5x – 6
Factorise:
x3 – 2x2 – x + 2
Factorise:
x3 – 3x2 – 9x – 5
Find the factor of the polynomial given below.
`sqrt 3 x^2 + 4x + sqrt 3`
Factorize the following polynomial.
(x2 – x)2 – 8 (x2 – x) + 12
The factorisation of 4x2 + 8x + 3 is ______.
Which of the following is a factor of (x + y)3 – (x3 + y3)?
Show that p – 1 is a factor of p10 – 1 and also of p11 – 1.
Without finding the cubes, factorise:
(x – 2y)3 + (2y – 3z)3 + (3z – x)3
