Advertisements
Advertisements
Question
Determine the following polynomial has (x + 1) a factor:
`x^3-x^2-(2+sqrt2)x+sqrt2`
Solution
If(x + 1) is a factor of polynomial `p(x) = x^3-x^2-(2+sqrt2)x+sqrt2`, then p(−1) must be zero, as a result (x + 1) is not a factor of this polynomial.
`p(-1) = (-1)^3 - (-1)^2 - (2+sqrt2)(-1) + sqrt2`
= `-1-1+2+sqrt2+sqrt2`
= `2sqrt2`
As p(−1) ≠ 0,
Therefore, (x + 1) is not a factor of this polynomial.
APPEARS IN
RELATED QUESTIONS
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 value of k, if x – 1 is a factor of p(x) in the following case:
p(x) = `2x^2+kx+sqrt2`
Factorise:
6x2 + 5x – 6
Factorise:
2y3 + y2 – 2y – 1
If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is ______.
Find the value of m so that 2x – 1 be a factor of 8x4 + 4x3 – 16x2 + 10x + m.
Factorise:
x2 + 9x + 18
Factorise the following:
9x2 – 12x + 4
Factorise:
1 + 64x3
Find the following product:
(2x – y + 3z)(4x2 + y2 + 9z2 + 2xy + 3yz – 6xz)
