# 3x3 − X2 − 3x + 1 - Mathematics

3x3 − x2 − 3x + 1

#### Solution

Let f(x) = 3x^3 - x^2 - 3x + 1 be the given polynomial.

Now, putting  x = 1,we get

f(1) = 3(1)^3 - (1)^2 - 3(1) + 1

 = 3-1 -3 +1 = 0

Therefore, (x-1)is a factor of polynomial f(x).

Now,

f(x) = 3x^2 (x-1) + 2x(x-1)-1(x-1)

 = (x-1){3x^2 + 2x - 1}

 = (x-1 ){3x^2 + 2x -1}

= (x -1)(x+1)(3x-1)

Hence (x -1),(x+1) and (3x - 1 )are the factors of polynomial f(x).

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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 6 Factorisation of Polynomials
Exercise 6.5 | Q 5 | Page 32

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