baby456
  • baby456
Please help me with factoring 10m^3n^2-15m^2n^1 medal + fan just don't just give me the answer. Explain IT.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
baby456
  • baby456
@mathstudent55
baby456
  • baby456
@dajakesta
mathstudent55
  • mathstudent55
\(\large 10m^3n^2-15m^2n^1\) You are factoring a two-term polynomial. Start by factoring a common factor out of both terms. What is the GCF of both terms?

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baby456
  • baby456
5
mathstudent55
  • mathstudent55
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?
baby456
  • baby456
6
mathstudent55
  • mathstudent55
Not a number. It's a variable to a power.
mathstudent55
  • mathstudent55
|dw:1435094377519:dw|
mathstudent55
  • mathstudent55
m^3 and m^2 have m^2 in common.
mathstudent55
  • mathstudent55
Then we see what n^2 and n^1 have in common. |dw:1435094442799:dw| n^2 and n^1 have n in common.
mathstudent55
  • mathstudent55
That means the GCF of the two terms is 5m^2n
baby456
  • baby456
how did you get 2 from
mathstudent55
  • mathstudent55
The common factor is \(\large 5m^2n\) The 2 is the exponent of the m.
baby456
  • baby456
ok
mathstudent55
  • mathstudent55
\(\large 10m^3n^2-15m^2n^1\) Now we factor out the GCF: \(\large =5m^2n(~~~~~~~~~~~~~~)\)
baby456
  • baby456
how? i dont know i am so confused
baby456
  • baby456
what gcf
mathstudent55
  • mathstudent55
\(\large =5m^2n(2mn - 3)\)
baby456
  • baby456
where are you getting the 2 and 3
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
Factoring is the opposite of the distributive property.
baby456
  • baby456
i dont get it
mathstudent55
  • mathstudent55
Let me go back a few steps and show a simple example. Do you know the distributive property?
baby456
  • baby456
what?
mathstudent55
  • mathstudent55
Use the distributive property to simplify this expression: \(2(3 + 5)\)
baby456
  • baby456
11 i think
mathstudent55
  • mathstudent55
No. I'll show you. The distributive property of multiplication over addition is this: \(2(3 + 5) = 2 \times 3 + 2 \times 5\)
mathstudent55
  • mathstudent55
|dw:1435095136526:dw|
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
Here is another example: |dw:1435095244847:dw|
baby456
  • baby456
ok
baby456
  • baby456
but how does that help with factoring.
mathstudent55
  • mathstudent55
Factoring is doing the distributive property in reverse.
mathstudent55
  • mathstudent55
Here is an example of the distributive property using variables. |dw:1435095365764:dw|
baby456
  • baby456
ok
mathstudent55
  • mathstudent55
We went from a product of a variable, m, and a binomial, 2m + n, to a result, \(2m^2 + mn\)
mathstudent55
  • mathstudent55
Now let's do that problem in reverse. Let's say we are given the final answer above, and we are asked to factor.
mathstudent55
  • mathstudent55
This is the problem we have now: |dw:1435095505073:dw|
mathstudent55
  • mathstudent55
First, we find the greatest common factor of the two terms.
mathstudent55
  • mathstudent55
|dw:1435095568553:dw|
mathstudent55
  • mathstudent55
Now we take the problem, and we do the distributive property in reverse.
mathstudent55
  • mathstudent55
We need to find what to place inside the parentheses to get back to our original problem. |dw:1435095632204:dw|
mathstudent55
  • mathstudent55
|dw:1435095685363:dw|
mathstudent55
  • mathstudent55
|dw:1435095737610:dw|
mathstudent55
  • mathstudent55
|dw:1435095761968:dw|
mathstudent55
  • mathstudent55
|dw:1435095800516:dw|
baby456
  • baby456
i dont get it. it like my brain is stuck.
mathstudent55
  • mathstudent55
This is the answer: |dw:1435095820650:dw|
mathstudent55
  • mathstudent55
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.
baby456
  • baby456
where did you get THAT HOW PROB ELM THE 2M THING.
mathstudent55
  • mathstudent55
Go over this a few times. Sometimes after you go over something a few times you begin to understand.
mathstudent55
  • mathstudent55
In the problem I made upi above, which is to factor \(2m^2 + mn\) Did you understand how I got the GCF of m?
mathstudent55
  • mathstudent55
|dw:1435096046142:dw|
baby456
  • baby456
no
baby456
  • baby456
where are you getting the 2 from
mathstudent55
  • mathstudent55
The GCF means the greatest common factor. It's the largest factor that two numbers have in common.
mathstudent55
  • mathstudent55
Which 2 are you asking about? Copy one of my drawings and circle the 2 you are asking about.
baby456
  • baby456
|dw:1435096203121:dw|