Advertisements
Advertisements
Question
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
Advertisements
Solution
If g(x) = x − 3 is a factor of the given polynomial p(x), then p(3) must be 0.
p(x) = x3 − 4x2 + x + 6
p(3) = (3)3 − 4(3)2 + 3 + 6
= 27 − 4(9) + 3 + 6
= 27 − 36 + 3 + 6
= 0
Hence, g(x) = x − 3 is a factor of the given polynomial.
APPEARS IN
RELATED 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 p(x) in the following case:
p(x) = `kx^2 - sqrt2x +1`
Factorize the following polynomial.
(x2 – 6x)2 – 8 (x2 – 6x + 8) – 64
Factorize the following polynomial.
(x2 – 2x + 3) (x2 – 2x + 5) – 35
x + 1 is a factor of the polynomial ______.
One of the factors of (25x2 – 1) + (1 + 5x)2 is ______.
The factorisation of 4x2 + 8x + 3 is ______.
Find the following product:
(2x – y + 3z)(4x2 + y2 + 9z2 + 2xy + 3yz – 6xz)
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
