Question

Check whether (3x-1) is a factor of 9x^3 -3x^3 +3x-1​

Answer 1

Answer:

let 3x-1 is factor

3x -1 = 0

x= 1/3

put in f(x)

9×1/27 - 3×1/27 +0

1/3 - 1/9

that is not = 0 answer is no

Answer 2

Answer:

$\large\boxed{\sf{Yes}}$

Step-by-step explanation:

Given expression:

$9 {x}^{3} - 3 {x}^{2} + 3x - 1$

For (3x-1) to be a factor, x = ⅓ should be the root of given expression.

$= > 3x - 1 = 0 \\ \\ = > x = \frac{1}{3}$

Therefore, we get,

$= 9 \times {( \frac{1}{3}) }^{3} - 3 {( \frac{1}{3} )}^{2} + 3( \frac{1}{3}) - 1 \\ \\ = \frac{9}{27} - \frac{3}{9} + 1 - 1 \\ \\ = \frac{9}{27} - \frac{3 \times 3}{9 \times 3} \\ \\ = \frac{9}{27} - \frac{9}{27} \\ \\ = 0$

Hence, (3x - 1) is the factor.