How to solve this type of question? (advanced functions)

[Joel]

Hi,
Can anyone tell me how to solve questions like this:

When ax³-x²​+2x+b is divided by x-1, the remainder is 10. When it is divided by x-2, theremainder is 51. Find the values of a and b.

I have no idea where to start , I probably can figure it out if someone can help get my started.
Fyi this is homework for grade 12 advanced functions. (there is no functions section, but I'm told calculus is similar, so hopefully I'm in the right forum)

Thanks for any and all reply's.

 

[fcabanski]

Recall or look up polynomial long division, or synthetic division.

http://www.sosmath.com/algebra/factor/fac01/fac01.html

http://www.purplemath.com/modules/synthdiv.htm

When you complete the division in each case, with x-1 and x-2, you'll have two equations with a and b in them. You can then solve those equations for a and b (simultaneous equations, or by adding or subtracting the equations to eliminate one of the variables).

It will be easier with synthetic division.

Hi,
Can anyone tell me how to solve questions like this:

When ax³-x²​+2x+b is divided by x-1, the remainder is 10. When it is divided by x-2, theremainder is 51. Find the values of a and b.

I have no idea where to start , I probably can figure it out if someone can help get my started.
Fyi this is homework for grade 12 advanced functions. (there is no functions section, but I'm told calculus is similar, so hopefully I'm in the right forum)

Thanks for any and all reply's.

 

[Joel]

Got it. Thanks