Factor And Remainder Theorem

Questions

6. When the polynomial 3x^2+ax^2+bx-1 is divided by x-2 the remainder is 5. When it is divided by x+1 the remainder is -1.
Find the values of a and b.

7. Solve the equations:
a) 3x^3-2x^2-11x+10=0
b) 2x^3+5x^2-14x-8=0
c) 4x^3+12x^2-7x-30=0

I have been studying how to use the factor theorem and algebraic long division, I was set these questions as part of a 2 hour assignment and I haven't got a clue on what to do.

I don't want solutions, I want to learn how to correctly work these out.

For question 6, you can subtract the equation by 5 in order to make x-2 become a factor of the equation you got and minus -1 in order to make x+1 become a factor of the equation you got. Then use the factor theorem to get a simultaneous equation.

Hint for 7a

Try f(1)

That's where I got to. F(2) = (a*4)+(b*2)=-18
And a-b=3

Where do I go from that?

So how does that help me find the other 2?

you can get a=3+b from a-b=3
then substitute a in the first equation

Since f(1) = zero you know that x-1 is a factor, this leaves you with a quadratic.

So how does that help me find the other 2?

For question 6 do the same again using -1 instead of 2, then use your two answers and solve as a simultaneous equation