Comments for Santa Barbara Math Tutor

Comment on Why it’s good to be confused by Algebra’s Negative Numbers by Kylie Batt

Kylie Batt — Wed, 05 May 2010 03:11:26 +0000

Я думаю, что Вы допускаете ошибку. Давайте обсудим это. Пишите мне в PM.... If you, or someone you know, is having difficulty “getting” negative numbers, be happy.....

Comment on A Cool Tip for Factoring Polynomials by Kylie Batt

Kylie Batt — Tue, 04 May 2010 01:50:10 +0000

По моему мнению Вы допускаете ошибку. Могу отстоять свою позицию.... It’s based on the realization that if one of your polynomial factors can be reduced, then so can your polynomial.....

Comment on Why it’s good to be confused by Algebra’s Negative Numbers by Kylie Batt

Kylie Batt — Thu, 22 Apr 2010 08:29:13 +0000

По моему мнению, это - большая ошибка.... If you, or someone you know, is having difficulty “getting” negative numbers, be happy.....

Comment on A method for using a negative base in a logarithm by Kylie Batt

Kylie Batt — Wed, 21 Apr 2010 09:59:22 +0000

Должен Вам сказать это – заблуждение….

Common wisdom says you can’t use a negative base in a logarithm if you’re working with real numbers
i.e…..

Comment on A method for using a negative base in a logarithm by Kylie Batt

Kylie Batt — Sat, 17 Apr 2010 00:29:46 +0000

Вы абсолютно правы. В этом что-то есть и мысль хорошая, согласен с Вами….

However, consider this
For every integer a, […….

Comment on Why it’s good to be confused by Algebra’s Negative Numbers by Kylie BattName

Kylie BattName — Mon, 12 Apr 2010 14:21:55 +0000

Так бывает.... Negative numbers are a [.......

Comment on Why it’s good to be confused by Algebra’s Negative Numbers by Kylie Batt

Kylie Batt — Sun, 11 Apr 2010 20:19:50 +0000

Блестяще... Negative numbers are a [.......

Comment on A method for using a negative base in a logarithm by Alex Gordon

Alex Gordon — Sat, 03 Apr 2010 10:04:34 +0000

Ничего подобного….

However, consider this
For every integer a, […….

Comment on A Cool Tip for Factoring Polynomials by admin

admin — Tue, 03 Nov 2009 01:19:00 +0000

John,

That is cool.

I had to prove to myself that it’s a valid approach, so here’s what I did:

Assuming that ax^2 +bx + c can be factored into (ex + g) * (hx + k), we get

ax^2 + bx + c = ehx^2 + ekx + ghx + gk, which tells us that
a = eh
b = ek + gh, and
c = gk

Multiplying a times c yields
ac = ehgk, which can be rewritten as

ek = ac/gh

substituting this value for ek into the equation for b
b = ac/gh + gh

The right side of the equation is the sum of the factors of ac, so we can read this as saying that the coefficient of b is the sum of the factors of ac, which is the basis of your procedure.

thanks

Comment on A Cool Tip for Factoring Polynomials by John Dent

John Dent — Sat, 31 Oct 2009 16:07:08 +0000

Another cool way is…
Example 13: 6×2 + 19x + 10
Check for a common factor. Since there isn’t any:

Multiply the (6)(10) = 60 and list all factors that are reasonable: (6)(10), (-6)(-10), (5, 12), (4, 15)
The sum of (4, 15) is 19 so that is what we want.
Rewrite 6 x2 + 19x + 10 as (by breaking 19x into 4x+15x for grouping)

6×2 + 4x + 15x + 10 = 2x(3x + 2) + 5(3x + 2) = (3x + 2)(2x + 5).

In the example you did 6×2 – 7x – 20

Multiply (6)(-20)= -120 and list the factors that are reasonable (and maybe add up to -7)
(15)(-8), (-15)(8)

The sum of -15 and 8 is what we want because it is -7, so we rewrite the original equation as

6×2 -15x +8x-20 and then group to factor.

3x(2x-5)+4(2x-5) which can then be written (3x+4)(2x-5)