Someone I know IRL recently wrote, “I didn’t use algebra at all today.” That was probably not true, but no matter.
The Daughter is studying algebra right now in 8th grade and it’s a real PITA. Because she was so good in 7th grade math, she skipped over 8th grade math, what that was, and is now taking the math for 9th grade. This is a problem because she doesn’t know, and I surely don’t remember, what she’s missing.
I should note that when I was in 9th grade, I was very good in algebra. I remember helping a fellow student, Sid, at the chalkboard, when Miss McNulty couldn’t get him to understand.
I got a 97 in the Regents final. (Yes, I remember this; no I didn’t look it up. I got 86 in geometry and 98 is trigonometry.) But that was a HALF CENTURY AGO. THAT will make you feel old.
I have been depending on something called Tiger Algebra to help her muddle through.
For the problem 10x^2+x-21=0, where the ^ over the 6 key represents “power of,” so ten X squared in this case.
The factoring is the tough part to explain.
Factoring 10x^2+x-21
The first term is 10x^2 – its coefficient is 10
The middle term is +x its coefficient is 1
The last term, “the constant”, is -21
Step-1 : Multiply the coefficient of the first term by the constant 10 • -21 = -210
Step-2 : Find two factors of -210 whose sum equals the coefficient of the middle term, which is 1 .
-210 + 1 = -209
-105 + 2 = -103
-70 + 3 = -67
-42 + 5 = -37
-35 + 6 = -29
-30 + 7 = -23
-21 + 10 = -11
-15 + 14 = -1
-14 + 15 = 1 That’s it
By “it,” we’re talking the very beginning of “it.”
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -14 and 15
10x^2 – 14x + 15x – 21
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (5x-7)
Add up the last 2 terms, pulling out common factors :
3 • (5x-7)
Step-5 : Add up the four terms of step 4 :
(2x+3) • (5x-7)
Which is the desired factorization
At which point you take 2x+3=0 and 5x-7=0, and get 1.5 and 1.4 respectively, then do a whole bunch of other stuff with graphing designed to make your eyes glaze over.
We usually work on this in the morning, after the Daughter has felt despair the night before, which means doing it in lieu of me blogging in the morning, which is my best time for writing.
And she SORT OF understands parts of this. Hey, if you have an easier way to find the factors, please let me know. My blog will thank you, publicly if you want.
Eyes glazing over, yes. I see random numbers scrawled thru the middle of your article, but I just slid over it becauset’s all totally meaningless to me, just a number salad. My mind doesn’t work that way. Likewise trying to read a “lay-oriented” book on cosmological physics book last night. Give me something in the humanities, wonderful, but mathematics? Pfft.
I feel her pain. You and Mom were the brainy math ones in the family…I am not….much love to her,and bless you for being there for her to help her try to muddle through….xoxo
Back in the Old Silurian times, we were expected to plug those variables into a scary-looking formula.
https://en.wikipedia.org/wiki/Quadratic_formula
(Or, for more difficult problems, you can use the quadratic equation on the back of the page so you have an idea where you’re headed, and then work backwards.
Or, if she’s really good at basic algebra, step two can be shortened to the problem:
a*b = -210
a+b = 1
But there might be rules she needs to follow common core.)
O M G This caused a flashback to 1964! I can still feel the panic that hit each and every time I entered Mr. Turbide’s classroom. Algebra followed French I with Miss Callahan. Those two hours each and every day of the week gave me nightmares!
I was so bad at Algebra I failed the class and had to repeat it the following year! Ah, The Horror!