Advertisements
Advertisements
Question
If (x − 1) is a factor of polynomial f(x) but not of g(x) , then it must be a factor of
Options
f(x) g(x)
−f(x) + g(x)
f(x) − g(x)
\[\left\{ f(x) + g(x) \right\} g(x)\]
Solution
As (x -1)is a factor of polynomial f(x) but not of g(x)
Therefore f(1) = 0
Now,
Let p(x) = f(x).g(x)
Now
`p(1) = f(1) .g(1)`
`p(1) = 0 0.g(1)`
` = 0`
Therefore (x − 1) is also a factor of f(x).g(x).
APPEARS IN
RELATED QUESTIONS
Write the coefficient of x2 in the following:
`pi/6x^2- 3x+4`
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
`r(x)=3x^2+4x^2+5x-7`
Find the remainder when x3 + 3x2 + 3x + 1 is divided by \[x + \pi\] .
f(x) = 3x4 + 17x3 + 9x2 − 7x − 10; g(x) = x + 5
3x3 − x2 − 3x + 1
Mark the correct alternative in each of the following:
If x − 2 is a factor of x2 + 3ax − 2a, then a =
If x + 1 is a factor of the polynomial 2x2 + kx, then k =
Let f(x) be a polynomial such that \[f\left( - \frac{1}{2} \right)\] = 0, then a factor of f(x) is
Factorise the following:
z² + 4z – 12
Factorise the following:
8m3 – 2m2n – 15mn2
