Question

show that (x-2)is a factor of polynomial F(x)= 2x-3x-17x+30 hance factories F(x)

Answer 1

$\textbf{ Hello Mate! }$

If ( x - 2 ) is factor of f(x) means that value of x = 2

$f(x) = 2 {x}^{3} - 3 {x}^{2} - 17x + 30 \\ f(2) = 2 {(2)}^{3} - 3( {2)}^{2} - 17(2) + 30 \\ = 16 - 12 - 34 + 30 \\ = 46 - 46 = 0$
Hence, f(x) = 0 which proves that ( x - 2 ) is factor of f(x)

Now, let's divide (x-2) from f(x) manually

Please refer to attatchment

Have great future ahead!