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\(\large 10m^3n^2-15m^2n^1\) You are factoring a two-term polynomial. Start by factoring a common factor out of both terms. What is the GCF of both terms?
Correct. For the number parts, 10 and -15, you can factor out 5. What about for the variable parts? What do m^3 and m^2 have in common?
Not a number. It's a variable to a power.
m^3 and m^2 have m^2 in common.
Then we see what n^2 and n^1 have in common. |dw:1435094442799:dw| n^2 and n^1 have n in common.
That means the GCF of the two terms is 5m^2n
how did you get 2 from
The common factor is \(\large 5m^2n\) The 2 is the exponent of the m.
\(\large 10m^3n^2-15m^2n^1\) Now we factor out the GCF: \(\large =5m^2n(~~~~~~~~~~~~~~)\)
how? i dont know i am so confused
\(\large =5m^2n(2mn - 3)\)
where are you getting the 2 and 3
The 2 and the 3 are the numbers you need so that when you multiply by the 5 outside you get back the 10 and 15 you started with.
Factoring is the opposite of the distributive property.
i dont get it
Let me go back a few steps and show a simple example. Do you know the distributive property?
Use the distributive property to simplify this expression: \(2(3 + 5)\)
11 i think
No. I'll show you. The distributive property of multiplication over addition is this: \(2(3 + 5) = 2 \times 3 + 2 \times 5\)
The distributive property shows you that you multiply the number outside parentheses by each of the numbers inside the parentheses. The you add the products.
Here is another example: |dw:1435095244847:dw|
but how does that help with factoring.
Factoring is doing the distributive property in reverse.
Here is an example of the distributive property using variables. |dw:1435095365764:dw|
We went from a product of a variable, m, and a binomial, 2m + n, to a result, \(2m^2 + mn\)
Now let's do that problem in reverse. Let's say we are given the final answer above, and we are asked to factor.
This is the problem we have now: |dw:1435095505073:dw|
First, we find the greatest common factor of the two terms.
Now we take the problem, and we do the distributive property in reverse.
We need to find what to place inside the parentheses to get back to our original problem. |dw:1435095632204:dw|
i dont get it. it like my brain is stuck.
This is the answer: |dw:1435095820650:dw|
The way you check the answer is to multiply it out using the distributive property to make sure you get back to the given problem.
where did you get THAT HOW PROB ELM THE 2M THING.
Go over this a few times. Sometimes after you go over something a few times you begin to understand.
In the problem I made upi above, which is to factor \(2m^2 + mn\) Did you understand how I got the GCF of m?
where are you getting the 2 from
The GCF means the greatest common factor. It's the largest factor that two numbers have in common.
Which 2 are you asking about? Copy one of my drawings and circle the 2 you are asking about.