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### Course: Digital SAT Math>Unit 8

Lesson 1: Factoring quadratic and polynomial expressions: medium

# 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
• 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
• These guys are making it way too complicated.
• 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 .
• 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?
• 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
• Man guys I just dont get this at all
• factoring is so hard for me. any suggestions?
• I know factoring but i sometimes end up with the wrong answer
• (p+1)^2 can be factored as (p^2+2p+1^2)?
• 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).