Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,455

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

؟؟؟

One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,455

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

:Dthanx

One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,455

I am watching it now!

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

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

One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

13. x^2 14x + 49 is it b????

A(-x 7)(-x 7)

B(x + 7)(x 7)

C(x + 7)(x + 7)

D(x 7)(x + 7)

E(x 7)(x 7)

FThis polynomial cannot be factored by using the perfect squares method.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,455

Hi;

Nope. It cannot be B.

**In mathematics, you don't understand things. You just get used to them.**

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

how do u do these there confusingggggg

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,455

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?

**In mathematics, you don't understand things. You just get used to them.**

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

so its <a >???

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,455

Hi;

It is E.

**In mathematics, you don't understand things. You just get used to them.**

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

its e but why am stilll reallly confused

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,455

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

**In mathematics, you don't understand things. You just get used to them.**

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

oooh ok thats easy ill do the rest on my own thanx allot

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,455

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?

**In mathematics, you don't understand things. You just get used to them.**

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

yeah they didnt teach us that

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,455

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

**In mathematics, you don't understand things. You just get used to them.**

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

no am doing the rest of the questions and yeah i would love 2 know how to do the way

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

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.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,455

Hi;

Yes, that is A.

Here is FOIL:

FOIL stands for

F is first

O is outer

I is inner

L is last

To multiply two binomials:

( x - 7 ) ( x - 7 )

Take F ( first ) which is the two x's. x * x = x^2,

Now take O ( outer ) which is x * -7 = - 7 x

Now take inner which is the -7 * x = - 7 x

Now take the last. Which is -7 * -7 = 49

Add them all up:

Using these ideas you can check many problems on your own.

**In mathematics, you don't understand things. You just get used to them.**

Offline

**zee-f****Member**- Registered: 2011-05-12
- Posts: 1,220

wow thanx

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,455

I have to go now, I will see you later.

**In mathematics, you don't understand things. You just get used to them.**

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,528

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 (2011-07-23 07:44:27)*

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,528

hi again,

Whilst I was typing that you and bobbym seem to have moved on.

FOIL. I've not been taught that but my picture method is the same thing with pictures. (You'll discover I do lots of maths with pictures!)

Say you wanted (2x + 3)(5x + 7)

see picture.

F = 2x times 5x

O = 2x times 7

I = 3 times 5x

L = 3 times 7

So we get

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline