Math Is Fun Forum

I think you're getting the quadratic formula wrong...

I went back to this question and tried it out myself.
firstly I divide f(x) by one of the factors (x + 1).   Then I take the quotient and divide that by the other factor (x - 1).  I am now left with the quadratic 3x^2 + 7x + 4 which I factorise into (3x + 4) and (x + 1).
Thus the factors are:
(3x + 4)(x - 1)(x + 1)(x + 1) == (3x + 4)(x - 1)(x + 1)^2
 
  As always, thanks for the help

If you have one cake and divide between people they get half each - this is fractions.  2 x 1/2 = 1 (two halfs equal one whole).  Another way to look at it is to say they get 50% each because just as 1/1 is a whole cake, 100% is also the whole cake.  Since 50 is half of one hundred and they each get half of the cake, they are receiving 50% of the cake each.
   You can also look at it as 1/2 (one divided by two) = 0.5!   1.00 is the whole cake and 0.50 is half of it i.e. 50%.
   Go to www.google.com and have a look for GCSE mathematics material and I'm sure you will come up trumps.

P.S. GCSE is the british exams that all state school children take at around 16 years of age.

how do I divide f(x) by x^2-1?

Nope, no idea

I just looked at what I could do to (x - 1) to make (x^2 - 1).  I only got (x - 1) in the first place beause I misread the book! So that was luck, then fgarb pointed out that it was one of the factors anyway.

f(1) = 3(1)^4 + a(1)^3 + b(1)^2 - 7(1) - 4 = 0
                                                      a + b = 8

f(-1) = 3(-1)^4 + a(-1)^3 + b(-1)^2 - 7(-1) - 4 = 0
                                                           -a + b = -6

Thus: a = 7 and b = 1.
How do I go about factorising f(x) now?  Do I use the same long division method I have been using on cubic polynomials?

I do indeed know how to find a and b if I have two factors but I really have no idea how to get the second factor.  What must I do to x - 1 to make x^2 - 1?
  Maybe I must simply guess the other factors and put them into f(x) and test different values of a and b from f(1) till I find another that makes f(x) = 0?

(x^2 - 1) / (x - 1) = ???

That is the question, aye.  The other questions give you two factors to work from.  Let my type the question exactly as it is written (I've just noticed somthing that I did not see before as it was smudged over with ink!);

"Given that (x² - 1) is a factor of the polynomial f(x), where f(x) = 3x^4 + ax^3 + bx^2 - 7x - 4, find the values of a and b and hence factorise f(x) completely."

I'm assuming that the x² instead of simply x in the factor plays a vital role here, I have not seen this before.

what does the % operator do?

y = -1/x rotates the curve in the x-axis
and
y = 4/x scales in the y-direction
are the "correct" answers shown in my a-level book. I don't see why they switch between y and x axis?

Where did you learn maths Old_dad?

so y=2x² doubles each y co-ord and since y=1/2x² halfs each, that has the same effect as doubling each x co-ord?
With a curve of y=1/x, it gets scaled in both directions when the integer(1) there changes?