Advertisements
Advertisements
Question
f(x) = 2x3 − 9x2 + x + 12, g(x) = 3 − 2x
Advertisements
Solution
It is given that f(x) = 2x3 − 9x2 + x + 12 and g(x) = (3 − 2x)
By factor theorem, (3 − 2x) is the factor of f(x), if f(3/2)= 0
Therefore,
In order to prove that (3 − 2x) is a factor of f(x). It is sufficient to show that `f(3/2) = 0`
Now,
`f(3/2) = 2(3/2)^3 -9(3/2)^2 +(3/2) + 12`
` = 27/4 - 81/4 + 3/2 + 12`
` = 54 / 4 + 3/2 + 12`
` = -27/2 + 3/2 +12`
` = -12 + 12`
`= 0`
Hence, (3 − 2x), is the factor of polynomial f(x).
APPEARS IN
RELATED QUESTIONS
Write the degrees of the following polynomials:
`12-x+2x^3`
Write the degrees of the following polynomials:
7
Identify polynomials in the following:
`q(x)=2x^2-3x+4/x+2`
If the polynomials 2x3 + ax2 + 3x − 5 and x3 + x2 − 4x +a leave the same remainder when divided by x −2, find the value of a.
2x4 − 7x3 − 13x2 + 63x − 45
If x + 2 is a factor of x2 + mx + 14, then m =
If (x − 1) is a factor of polynomial f(x) but not of g(x) , then it must be a factor of
Factorise the following:
2a2 + 9a + 10
Factorise the following:
m2 + 2mn – 24n2
If x + 2a is a factor of x5 – 4a2x3 + 2x + 2a + 3, find a.
