Question

Check whether the polynomial 3x-1 is a factor of 9x^3-3x^2+3x-1 ​

Answer 1

\left[x _{2}\right] = \left[ \frac{1}{6}+\left( \frac{-1}{6}\,i \right) \,\sqrt{11}\right][x

2

]=[

6

1

+(

6

−1

i)√

11

]

Answer 2

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

Factorise The Terms

9x³-3x²=3x²(3x-1)

$( {9x}^{3} - {3x}^{2} )+ 3x - 1 \\ \\ {3x}^{2} (3x - 1) + 3x - 1 \\ \\ {3x}^{2} (3x - 1) + 1(3x - 1) \\ \\ ( {3x}^{2} + 1)(3x - 1)$

Two Factors of 9x³-3x²+3x-1

=(3x²+1)(3x-1)

So, 3x-1 is one of The Factor of Given Polynomial