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## 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

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# 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)

## Video 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.