Advertisements
Advertisements
Questions
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 x2 + x + k.
Advertisements
Solution
If x − 1 is a factor of polynomial p(x), then p(1) must be 0.
p(x) = x2 + x + k
p(1) = 0
⇒ (1)2 + 1 + k = 0
⇒ 2 + k = 0
⇒ k = −2
Therefore, the value of k is −2.
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 factor of the polynomial given below.
`sqrt 3 x^2 + 4x + sqrt 3`
Show that 2x – 3 is a factor of x + 2x3 – 9x2 + 12.
Determine which of the following polynomials has x – 2 a factor:
3x2 + 6x – 24
Factorise the following:
1 – 64a3 – 12a + 48a2
Factorise:
1 + 64x3
Factorise:
`a^3 - 2sqrt(2)b^3`
Factorise:
a3 – 8b3 – 64c3 – 24abc
Without finding the cubes, factorise:
(x – 2y)3 + (2y – 3z)3 + (3z – x)3
