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### Course: Algebra basics>Unit 7

Lesson 7: Factoring quadratics: Difference of squares

# Factoring difference of squares: shared factors

Sal finds the binomial factor shared by m^2-4m-45 and 6m^2-150.

## Want to join the conversation?

• What do I do in a problem like:
108-3x^2
Where there isn't a perfect square for 108 or 3?
Thank you.
• if you factor out the common factor of 3 first, you get 3(36-x^2) which you can factor into 3(6-x)(6+x)
• I didn't understand the video...could someone please explain it again
• We are looking, for a "shared factor" since a factor is, a number/quantity that when multiplied with another produces a given number or expression it should then be shared by both the given quadratic expressions:

m^2-4m-45 and 6m^2-150

The factorization of m^2-4m-45 is = (m+5)(m-9)

And the factorization of 6m^2-150 is: 6(m+5)(m-5)

If you look closely at the factorization of each expression you will see that they share the factor (m+5). What we are looking for is precisely that, the binomial factor they share.
• Sal has excellent handwriting.
• Ik right.
(1 vote)
• Does anyone know how to do this: 2xsquare + 2x = 4
I don't seem to find any videos on these in Khan Academy...
If anyone knows where, please tell me. THANKS!
• Notice that the coefficients(the numbers before your x variables) are factor-able by 2. This means you can divide both sides of your expression by two so that you are left with x^2+x=2. You can then subtract 2 from both sides so that you are left with x^2+x-2=0. You can either use the quadratic formula to solve or factor your polynomial into (x+2)(x-1)=0. The solutions are x=-2 and x=1
• Could any help me with this? I'm having a hard time figuring this out.
A man invests \$2,400, some at 9.5% annual interest and the balance at 7% annual interest. If he receives \$208 in interest, how much did he invest at each rate?

(P.S. If someone knows where these problems are on Khan Academy, let me know.)
Thanks!
• Let x = dollars invested at 9.5%
Let y = dollars invested at 7%
\$2400 is the total invested, and total tells us to add. This means `x + y = 2400`

Next, I'm assuming you are working with simple interest.
Interest = Amount invested (Percent) (Time).
The 208 is total interest, so again, this means we add.
Interest at 9.5% + Interest at 7% = 208
Use the formula for interest for each component and you get the equation: `0.095x + 0.07y = 208`

You now have a system of linear equations that can be solved with elimination or substitution.
Let's use substitution.
Solve for y in `x+y = 2400` and you get `y = 2400 -x`
Substitute: ` 0.095x + 0.07(2400 - x) = 208`
Now solve for "x"
Distribute: ` 0.095x + 168 - 0.07x = 208`
Simplify: ` 0.025x + 168 = 208`
Subtract 168: ` 0.025x = 40`
Divide by 0.025: `x = 1600`
Find "y": `y = 2400 - 1600' `y = 800`

Thus, \$1600 was invested at 9.5% and \$800 was invested at 7%
Hope this helps. I haven't seen any videos on this site with problems like this. They have videos on solving systems of equations. You can try an internet search for system of equations problems involving interest.
• In the exercise below, I tried to solve by stating with -7 like so.

-7(-4 + x^2) = -7(-2^2 + x^2) = then tried to apply difference of squares like so -7(-2+x)(-2-x) which I though was correct but was not. the correct answer was not -7 but 7 and the final result was 7(2+x)(2-x). did I picked the wrong number as -7? I think 7 or -7 should not make any difference!

28−7x^2
• You have a sign error going from: -7(-2^2 + x^2) to -7(-2+x)(-2-x). Notice, the binomial has a positive x^2. Your factors create a negative x^2. You could have reversed the 2 terms to: -7(x^2-2^2). Then it's more obvious to see that both x's should be positive in your factors.

Hope this helps.
FYI - It is a good habit to multiply your factors to confirm that they recreate the original polynomial. If they do, then you know the factors are good.
• what does the symbol between m and 2 above mean?
• It's hard to write exponents on a computer. So we use the caret symbol ^

It just means m is being raised to the 2nd power.
• when do i use this in life that is not to pass a test? give me a real life example
(1 vote)
• essentially all forms of advanced math are useless depending on what future career you plan on taking.
For example, knowing Geometry is good but will prove useless in a field of fiction book writing, but can prove very useful in space travel and weather patterns.

So basically, you will be taught this stuff, but the likelihood you will ever use it in real life for a future career you take is likely. It's like an emergency kit in case you do need it.