Cubic and Quartic Functions Problems: Part 1

• Apr 26th 2011, 09:10 PM
theleontan
Cubic and Quartic Functions Problems: Part 1
I am having trouble with a couple of questions in terms of the proccess of solving the questions:
1 If x-3 is a factor is x^2+ax+b, then 3a+b+10 equals?
2 The x-axis intercepts of the graph with equation y=(x+a)^2(x^2-b^2), where a and b are positive constants are?

I will be greatly apprecieated if any of you would have the time to help and explain these questions for me.
• Apr 26th 2011, 09:17 PM
pickslides
This is a long list, so lets take them 1 at a time.

Quote:

Originally Posted by theleontan
I am having trouble with a couple of questions in terms of the proccess of solving the questions:
1 If x-3 is a factor is x^2+ax+b, then 3a+b+10 equals?

If x-3 is a factor then f(3)=0, does that help?
• Apr 26th 2011, 10:10 PM
theleontan
Care to explain? I still don't see how that helps :/
• Apr 27th 2011, 04:55 AM
earboth
Quote:

Originally Posted by theleontan
Care to explain?

If you have a term in x which consists of a factor (x-3) and an additional factor in x you can express this situation as:

http://latex.codecogs.com/png.latex?...-3) \cdot P(x)

If you plug in x = 3 then you get

http://latex.codecogs.com/png.latex?...=0} \cdot P(3) which is obviously zero.

Quote:

I still don't see how that helps :/
According to the text of your question

http://latex.codecogs.com/png.latex?T(x)=x^2+ax+b and http://latex.codecogs.com/png.latex?T(3) = 0

That means: Plug in x = 3 and see what you can say about the term you'll get.