Main content
SAT (Fall 2023)
Course: SAT (Fall 2023) > Unit 10
Lesson 2: Passport to advanced mathematics- Solving quadratic equations — Basic example
- Solving quadratic equations — Harder example
- Interpreting nonlinear expressions — Basic example
- Interpreting nonlinear expressions — Harder example
- Quadratic and exponential word problems — Basic example
- Quadratic and exponential word problems — Harder example
- Manipulating quadratic and exponential expressions — Basic example
- Manipulating quadratic and exponential expressions — Harder example
- Radicals and rational exponents — Basic example
- Radicals and rational exponents — Harder example
- Radical and rational equations — Basic example
- Radical and rational equations — Harder example
- Operations with rational expressions — Basic example
- Operations with rational expressions — Harder example
- Operations with polynomials — Basic example
- Operations with polynomials — Harder example
- Polynomial factors and graphs — Basic example
- Polynomial factors and graphs — Harder example
- Nonlinear equation graphs — Basic example
- Nonlinear equation graphs — Harder example
- Linear and quadratic systems — Basic example
- Linear and quadratic systems — Harder example
- Structure in expressions — Basic example
- Structure in expressions — Harder example
- Isolating quantities — Basic example
- Isolating quantities — Harder example
- Function notation — Basic example
- Function notation — Harder example
© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice
Structure in expressions — Basic example
Watch Sal work through a basic Structure in expressions problem.
Want to join the conversation?
I know how to factor just fine, but its my intuition that fails me. I wouldn't know what the first step to solving this would be(6 votes)- Isn't the answer -8, but not 8 as it mentioned in the video? Because, having formula ax^2+bx+c ( in our example x^2+8x+15), the sum of x1 and x2 must be equal to -b ( in our example b+c=-8) Why then here we have +8 in the example?(5 votes)
This can work however -b/a would be equal to -b-c because the roots are -b and -c, not b and c.
-b-c = -8
b+c = 8(1 vote)
Whenever you got algebra question or you're practicing algebra question open desmos graphing calculator in next tab
Now what we can do compare LHS AND RHS
L.H.S = 2x²+16x+30 = 2 (x²+8x+15)
R.H.S = 2(x+b)(x+c)*
Cancel 2 from booth side and we'll get
x²+8x+15 = x² + (b+c) + bc
Now Compare L.H.S and R.H.S
i.e. b+c = 8
This question is quite straightforward what if we got question like what's the value of bc + (b-c) or somthing that we need to find both constant
we can use the help of desmos which is built in graphing calculator inside bluebook app and also we can practice in their webside desmos.com
Now plot this eqn b+c = 8 and bc= 15 as x and y variables
x+y=8 & xy=15
Now,You can see intersecting point
(5,3) ==> (x,y) ==> (a,b)
Now you can get your answer a as 5 and b as 3 .(5 votes)- (p+1)^2 can be factored as (p^2+2p+1^2)?(4 votes)
Yes. expanding this equation makes it look like the below equation:
(p + 1) (p + 1)
(p + 1) (p + 1) = p^2 + p + p + 1^2 = p^2 + 2p + 1
Basically, the parentheses mean you are squaring the whole equation.
If you wanted to square P and 1 separately though, it would look more like this:
P^2 + 1^2 (which is simply P^2 + 1).(2 votes)
- hi asian here
just LCM the 15 after taking 2 common
3*5 = 15
now see that 3+5 is 8 which is what we need
now just calculate as 5x+3x
pure Nepali method
hope this helped(4 votes)- These guys are making it way too complicated.(1 vote)
- why couldnt it be answer C because that answer choice is the same thing, just simplified(2 votes)
i thought sum of roots of a quadriatic equation was -b/a?? How come we got 8?(1 vote)
Here b and c are not the roots of the quadratic equation( roots are -3 and -5), here we are comparing the equation on both sides and writing the values.(3 votes)
I never thought that Khan academy was same age as me(2 votes)
@1:34How did he know those two numbers would be b and c before factoring out the whole equation? 😫(1 vote)- how do I complete a section, I've watched the entire video(1 vote)
1:34Video transcript
- [Instructor] We're asked
in the equation above, b and c are constants. What is the value of b + c? And they give us the equation over here. So, pause this video and see
if you can have a go at that before we work through this together. All right, now let's work
through this together. And it looks like what's
happening is we have a quadratic on the left and then on the right we
have that same quadratic that is factored out, although they don't
tell us what b and c are we have to figure that out. So, one way to tackle this is
actually let me just rewrite the left-hand side of this. So, it is 2x squared + 16x + 30. And what I wanna do is try to get as close to the form that I have
on the right as possible. So, it looks like they factored out a two. So, let me do that. So, this is equal to two times. And if any of this factoring of quadratics is unfamiliar to you, I encourage you to review
that on Khan Academy, on The non-ACT portion of Khan
Academy to get the basics. But if we factor out of
two out of this first term, you're just left with an X squared. You factor out of two
out of 16x, you get 8x. And you factor a two out
of 30 and you get + 15. And then it looks like what they have done is they have factored this part into x + b X x + c. And the simplest way to factor
things is to say, all right, are there two numbers that
when I add them, I get eight, and that when I multiply them, I get 15? And those two numbers are
actually going to be b and c this is one of our main
factoring techniques. So, b + c needs to be equal to eight, and b X c needs to be equal to 15. And if we figure that out,
then we can factor completely. Well, we've just actually
answered their question, b + c needs to be equal to eight. And so, eight is the answer. Now, let me just factor
this out completely, so that you can see that a
little bit more completely. I'm using the word completely a lot. So, if I were to factor this out, this is the same thing as two times the two numbers
that add up to eight. And when I multiply them, I get 15, let's see three and five seemed to work. So, it's gonna be two times X plus three times X plus five. You can verify that three times five you're gonna get that 15 there. And then when you multiply
these two binomials, you're gonna get 3x + 5x, which is going to be 8x. And so, you can see that you
can either treat b as three and c is five or b is five and c is three, but either way, b + c is
going to be equal to eight.