Algebra II
-
California Standards Test: Algebra II
-
California Standards Test: Algebra II (Graphing Inequalities
-
CA Standards: Algebra II (Algebraic Division/Multiplication)
-
CA Standards: Algebra II
-
Algebra II: Simplifying Polynomials
-
Algebra II: Imaginary and Complex Numbers
-
Algebra II: Complex numbers and conjugates
-
Algebra II: Quadratics and Shifts
-
Examples: Graphing and interpreting quadratics
-
Algebra ||: Conic Sections
-
Algebra II: Circles and Logarithms
-
Algebra II: Logarithms Exponential Growth
-
Algebra II: Logarithms and more
-
Algebra II: Functions, Combinatorics
-
Algebra II: binomial Expansion and Combinatorics
-
Algebra II: Binomial Expansions, Geometric Series Sum
-
Algebra II: Functions and Probability
-
Algebra II: Probability and Statistics
-
Algebra II: Mean and Standard Deviation
Algebra II: Simplifying Polynomials 17-22, simplifying polynomials and algebraic expressions
⇐ Use this menu to view and help create subtitles for this video in many different languages.
You'll probably want to hide YouTube's captions if using these subtitles.
- We're on problem 17.
- And it asks us which expression shows the complete
- factorization of 12x squared minus 147?
- Let's see, first of all, can we factor out?
- 147 is a strange looking number.
- Let's see if we can factor out something.
- It's definitely not divisible by 12, because
- 12 goes into 144.
- Is it divisible by 3?
- 1 plus 4 is 5, 5 plus 7 is 12, and 12 is divisible by 3.
- And I don't know if you've seen that before.
- You just add up the digits and if that is divisible by 3,
- then the number's divisible by 3.
- So 147 is the divisible by 3.
- Let's see what it is.
- Let's work it out.
- It's 4 times 3 is 12, 27, it's 49.
- So we can factor 3 out of this.
- So then it becomes 3 times-- what's 12 divided by 3-- 4x
- squared minus-- 147 divided by 3, which we just
- figured out, was 49.
- And now this, once again, looks just like a squared
- minus b squared, where a would be 2x and b would be 9.
- So now we can factor that more.
- And I'll just switch colors arbitrarily.
- That becomes 3 times a plus b, so that would be 2x plus 7
- times a minus b.
- 2x minus 7.
- And that is choice D.
- In choice D, they wrote the 2x minus 7 first, but it's the
- same difference.
- So it's choice D.
- Problem 18.
- Let me see if I can get problem 18 going.
- Problem 18.
- Well, maybe I should cut and paste it.
- Why not?
- So I copied it and then let me paste it here.
- That's the problem.
- I'll rewrite it because I don't if that's big enough for
- you to see.
- So it says x plus 3 over x plus 5 plus 6 over x squared
- plus 3x minus 10.
- So when you add fractions, whether you're doing it with
- algebraic fractions or regular fractions, you have to find a
- common denominator.
- And let's see, we have to find the least common multiple of
- the denominators here, but I have a suspicion that this x
- plus 5 goes into this.
- So let's see if I can factor this.
- What two numbers, when I multiply them, equal minus 10,
- and when I add them equal plus 3?
- Let's see.
- Well, 5 times what is minus 10?
- It's 5 times minus 2 and 5 plus minus 2 is 3, so that
- works. x minus 2.
- So this is actually our least common multiple.
- This expression right here.
- So let me write it that way.
- So that is equal to-- I'm just going to rewrite this as x
- plus 5 over x minus 2.
- Now, x plus 3 over x plus 5, if we were to multiply both of
- those times x minus 2 to get something in this form, this x
- plus 3 over x plus 5 is the same thing as x plus 3 times x
- minus 2 over x plus 5 times x minus 2, right?
- You could just cancel this out right here and
- you'd get back to that.
- And now we're adding that.
- We're adding this term to this term.
- 6 over this, well, this is the same thing as this, so that's
- just plus 6.
- And now we just get into simplification mode.
- So x times x is x squared.
- x times minus 2 is minus 2x.
- 3 times x is plus 3x.
- 3 times minus 2 is minus 6, so that's this term right here.
- Got us that.
- And then we have the plus 6.
- And then all of that is over this stuff.
- And I look at the choices and it seems like they have it in
- this form, so I'll just write it in that form.
- x squared plus 3x minus 10.
- And let's see, the minus 6 and the plus 6 cancels out, and
- we're left with minus 2x plus 3x.
- So that's x squared-- minus 2 plus 3-- plus x over x squared
- plus 3x minus 10.
- And that is choice A.
- Choice A.
- Next problem.
- I'm almost out of space.
- I'll draw a line here, just so you don't get distracted.
- What is the simplified form of, and they write 3a squared
- b to the third, c to the minus 2, all of that over--
- interesting-- a to the minus 1 b squared c, and all of that
- is to the third power.
- So let's get in simplification mode.
- So this bottom part, we can re-simplify as-- let's see,
- maybe I wrote too big.
- 3a squared, b to the third, c to the minus 2.
- All of that, it's a to the negative 1, b squared, c to
- the third power, that's each of these items
- to the third power.
- So a to the minus 1 to the third power.
- You can multiply the exponents.
- That becomes a to the minus 3.
- I just took the negative 1 times the 3.
- b squared to the third power.
- That's b to the 2 times 3.
- That's b to the sixth power.
- And then finally c.
- Well, that's just c to the first of the third power, so
- that's c to the third.
- And now we can just say, well, this is the same thing.
- Let me switch colors.
- This color's getting mundane.
- This is equal to 3 times a to the 2-- we're dividing by a to
- the negative third-- so it's 2 minus minus 3.
- Let me write that, just so you understand-- 2 minus minus 3
- power-- that's where I got the 2; that's where I got the
- minus 3, and I subtracted because I'm dividing-- times b
- to the 3 minus 6, times c to the minus 2 minus 3.
- Once again, if we were multiplying these two, I would
- add the exponents.
- But anyway, let's simplify this.
- This equals 3a, 2 minus minus, so that's plus, 3a to the
- fifth, b to the minus 3, c to the minus 5.
- And this is the same thing as 3a to the fifth.
- b to the minus 3 is the same thing as 1 over b to the
- third, so over b to the third.
- And this is the same thing as 1 over c to the fifth.
- And that is choice A.
- Choice A.
- Next problem.
- Next problem.
- Oh, we already finished that page.
- All right.
- Let me copy and paste what they wrote.
- Let me put it at the top of this right there and paste it.
- That's what they're asking and I'll write it.
- 20x to the minus fourth over 27y squared
- divided by this fraction.
- So first of all, when you divide by a fraction, that's
- the same thing as multiplying by the inverse, right?
- So let's do that.
- I want to get rid of this pesky-looking division sign.
- So let's rewrite this as 20x to the minus fourth over 27y
- squared times-- instead of dividing by this, let's
- multiply by the inverse.
- So what's the inverse?
- 15y to the minus 5 over 8x to the minus 3.
- I just flipped it.
- All right?
- So let's see what we can do here.
- It seems like a lot of these numbers have common factors.
- Let's see, if we divide 15 by 3 and 27 by 3, so
- this becomes 5.
- 27 divided by 3 becomes 9.
- And just so you can think, you can view this as one
- continuous denominator or one continuous fraction.
- 20x to the minus 4 times-- well, now it's 5y to the minus
- fifth divided by 9y squared.
- Because when you multiply fractions, you just multiply
- the numerator times the numerator divided by the
- denominator times the denominator.
- Anyway, let's just keep simplifying.
- If you divide this by 4, you get 5.
- If you divide this by 4, you get 2.
- Let's see, I don't want to do too many steps all at once.
- You get 5x to the minus fourth times 5y to the minus fifth,
- all of that over 9y squared times 2x to the minus 3.
- So let's see.
- Let's get all the numbers out.
- So that is equal to 5 times 5 is 25 over 9 times 2 is 18
- times x-- let's do the x-- x to the minus 4-- minus because
- we're dividing-- minus 3.
- Minus minus 3 times y to the minus 5 minus 2, because we're
- dividing by that one.
- And that is equal to 25/18.
- Let's see, a minus minus, so that becomes a plus.
- Minus 4 plus 3, x to the negative 1, and then minus 5
- minus 2, y to the minus 7.
- This is the same thing as 1 over x to the 1.
- This is the same thing is 1 over y to the 7.
- So this is equal to 25 over 18x, 1
- over x, y to the seventh.
- y to the seventh in the denominator is the same thing
- as y to the minus seventh in the numerator.
- Anyway, that is choice-- let's see, 25 over 18--
- that is choice D.
- Choice D.
- And I'm out of time.
- See you in the next video.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
|
Have something that's not a question about this content? |
This discussion area is not meant for answering homework questions.
Discuss the site
For general discussions about Khan Academy, visit our Reddit discussion page.
Flag inappropriate posts
Here are posts to avoid making. If you do encounter them, flag them for attention from our Guardians.
abuse
- disrespectful or offensive
- an advertisement
not helpful
- low quality
- not about the video topic
- soliciting votes or seeking badges
- a homework question
- a duplicate answer
- repeatedly making the same post
wrong category
- a tip or feedback in Questions
- a question in Tips & Feedback
- an answer that should be its own question
about the site
Share a tip
Suggest a fix
Have something that's not a tip or feedback about this content?
This discussion area is not meant for answering homework questions.