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:Dthanx

me 2 he makes math fun lol but it didnt help me my problems start like this x^2-14x+49

Hi;

Nope. It cannot be B.

Hi zee-f;

Did you watch the video I gave you? There is a rule for them. But there are easier ways.

You have an x^2 so the first part of the factors has an x in both

(x +- ) ( x +- )

Now 49 is a square which factors to 7 * 7 and 1 * 49 but the middle term is -14 x so you pick one of those set of factors that sum to 14. Only 7 * 7 does that. Can you finish now?

Hi;

It is E.

Hi;

If the first and third terms are squares, figure out what they're squares of. Multiply those things, multiply that product by 2, and compare your result with the quadratic's middle term. If you've got a match, then you've got a perfect square.

Well, the first term, x^2, is the square of x. The third term, 49, is the square of 7 or -7. Multiplying, I get 7x. Multiplying this by 2, I get 14x. But the middle term is -14x so we use the -7 *x * 2 = -14x

So that is a perfect square and its factorization is (x-7)^2

Hi zee-f;

I think you are having difficulties because you do not know FOIL. That means you do not know yet know how to multiply two binomials. I am wondering why they skipped that?

Do you want to learn it? Are you tired or well rested?

14. x^2 + 18x + 81   does that make it a ??? cuz 81 = 9*9
and 9+9=18

A(x + 9)(x + 9)
B(-x + 9)(-x + 9)
C(x - 9)(x - 9)
D(x + 9)(x - 9)
E(x - 9)(-x + 9)
FThis polynomial cannot be factored by using the perfect squares method.

wow thanx

hi zee-f

I've not heard of the 'perfect squares method' but I think it means this:

Say a quadratic is like this one:

Take the middle term, half it, square the result.  (6/2 = 3.  3^2 = 9).  If the last term is that number then you can easily factorise like this:

see picture 2 (I loaded them the right way round but they've got reversed on the page.)

It would only work when half the middle number, squared is the last number.

So it would work for

and also for

If the squared term is not one x squared then it's more complicated.  see picture 1.

The clue that perfect squares might work is that it starts with 9 and ends with 25.  Both are perfect squares. (9=3x3   25=5x5)

But half the middle term squared isn't 25 this time. 

But if I make an adjustment it is ok.

9 is 3x3.

So take 30, half it then divide by 3, then square it.

So the extra step is divide by 3

So I think I can make a general rule.

If the quadratic is

(i) Check if both a and c are perfect squares.  If not, find another method.

(ii)  If they are, find the square root of 'a', let's call it 'r'.

(iii) Calculate b/2, then answer/r (call that 's'), then s squared.  If you've ended up with c then factorisation is:

Personally, I prefer to make a diagram like my pictures and slowly fit in all the numbers 'til I've got it.

Bob

Last edited by bob bundy (2011-07-24 05:44:27)