Advertisements
Advertisements
Question
f(x) = 3x3 + x2 − 20x +12, g(x) = 3x − 2
Advertisements
Solution
It is given that `f(x) = 3x^3 + x^3 - 20x + 12` and g(x) = 3x − 2
By the factor theorem,
(3x − 2) is the factor of f(x), if `f(2/3) =0`
Therefore,
In order to prove that (3x − 2) is a factor of f(x).
It is sufficient to show that `f(2/3) =0.`
Now,
`f(2/3) = 3(2/3)^3 + (2/3) ^2 - 20(2/3) +12`
`= 3(8/27) + 4/9 - 40/3 + 12`
` = 8/9 + 4/9 - 40 /3 + 12`
` = 12/9 - 4/3`
` = 4/3 - 4/3`
`= 0`
Hence, (3x − 2) is the factor of polynomial f(x).
APPEARS IN
RELATED QUESTIONS
Write the degrees of the following polynomials:
7
Identify polynomials in the following:
`g(x)=2x^3-3x^2+sqrtx-1`
\[f(x) = 3 x^4 + 2 x^3 - \frac{x^2}{3} - \frac{x}{9} + \frac{2}{27}, g(x) = x + \frac{2}{3}\]
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x + 1.
Find the remainder when x3 + 3x2 + 3x + 1 is divided by \[x + \pi\] .
The polynomials ax3 + 3x2 − 3 and 2x3 − 5x + a when divided by (x − 4) leave the remainders R1 and R2 respectively. Find the values of the following case, if R1 + R2 = 0.
f(x) = x3 − 6x2 + 11x − 6, g(x) = x2 − 3x + 2
If x + 2 is a factor of x2 + mx + 14, then m =
Factorise the following:
t² + 72 – 17t
Factorise the following:
12x2 + 36x2y + 27y2x2
