Thread: Cubic and Quartic Functions Problems: Part 1

1. 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.

2. This is a long list, so lets take them 1 at a time.

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?

3. Care to explain? I still don't see how that helps :/

4. 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:

$T(x)=(x-3) \cdot P(x)$

If you plug in x = 3 then you get

$T(3)=\underbrace{(3-3)}_{=0} \cdot P(3)$ which is obviously zero.

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

$T(x)=x^2+ax+b$ and $T(3) = 0$

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