Solving a Quadratic Equation: Finding All Linear Factors

[DumbKid88]

Ok this should be pretty simple math for you guys (Sophomore in HS)

Given that x-2 is a factor of P(x)=2x^3-3x^2-17x+30, find all other linear factors.

I started out doing synthetic division, and got 2x^2-x-19 with remainder -8. Shouldn't the remainder be zero since x-2 is a factor?

Please Help!

 

[Gokul43201]

Too tempted to make a dumb joke, but I'll wait.

PS: Dk88, welcome to PF! Are you having trouble posting? Have you read the forum guidelines?

 

[DumbKid88]

Sorry i accidentally posted it when I was just trying to preview it.

 

[SnipedYou]

Check your arithmetic $$-17 + 2 \ne -19$$

Then when you get a quadratic apply the quadratic formula.

 

[DumbKid88]

Check your arithmetic $$-17 + 2 \ne -19$$

Then when you get a quadratic apply the quadratic formula.

And that, my friend, is why my name is DumbKid. Ya -3 +4 surely is not -1. Thanx for the help.