Let p(x)=3x^3-4x^2-17x+6p(x)=3x3−4x2−17x+6.
To find whether or not (3x-1)(3x−1) is a factor of p(x)p(x), we have to
check whether p(1/3)p(13) is 0 or not.
p(1/3)=3(1/27)-4(1/9)-17(1/3)+6=1/9-4/9-17/3+6=-1/3-17/3+6=-6+6=0p(13)=3(127)−4(19)−17(13)+6=19−49−173+6=−13−173+6=−6+6=0
Hence, (3x-1)(3x−1) is a factor of p(x)p(x).
Now, p(x)=3x^3-4x^2-17x+6p(x)=3x3−4x2−17x+6.
=ul(3x^3-x^2)-ul(3x^2+x)-ul(18x+6).
=x^2(3x-1)-x(3x-1)-6(3x-1)
=(3x-1)(x^2-x-6)
Thus, (3x-1) is a factor of p(x), and, when p(x) is divided by
(3x-1), the quotient is (x^2-x-6).
Enjoy Maths.!
