Question Help

[MrBrillsbury]

Hey!

Can someone please explain how to solve this?

The polynomial f (x) = 2x^3 + ax^2 − bx + 3 has a factor x + 3. When f (x) is divided by
x − 2, the remainder is 15.

Thank you!

[Srd2000]

Hello, if you know that x-3 is a factor, then there is no remainder. So you can either divide f(x) by x+3, or even easier x+3=0 so f(3)=0. From this you can apply x-2=0 f(2)=15. Now you are left with simultaneous equations. Make sense from here?

f(x)=2x^3 +ax^2 -bx +3

f(-3) =0 =9a +3b -51
f(2) =15 =4a -2b +19

a=3, b=8

Hope this helps and is right