# F(X) = 3x3 + X2 − 20x +12, G(X) = 3x − 2 - Mathematics

f(x) = 3x3 + x2 − 20x +12, g(x) = 3x − 2

#### 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).

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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 6 Factorisation of Polynomials
Exercise 6.4 | Q 5 | Page 24