SOLUTION: Hi there, was wondering if someone could explain this for me? Explain the meaning of "factor of a polynomial" and explain the meaning "to factor a polynomial" thanks

Question 130497: Hi there, was wondering if someone could explain this for me?
Explain the meaning of "factor of a polynomial" and explain the meaning "to factor a polynomial"
thanks
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Remember, if you factor a number like 56, you simply break that number into it's product of prime numbers. So 56 factors to

56=2*2*2*7

So with polynomials, a similar thing occurs when you factor a polynomial

Looking at we can see that the first term is and the last term is where the coefficients are 1 and 6 respectively.

Now multiply the first coefficient 1 and the last coefficient 6 to get 6. Now what two numbers multiply to 6 and add to the middle coefficient 5? Let's list all of the factors of 6:

Factors of 6:
1,2,3,6

-1,-2,-3,-6 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 6
1*6
2*3
(-1)*(-6)
(-2)*(-3)

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to 5? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 5

First Number	Second Number	Sum
1	6	1+6=7
2	3	2+3=5
-1	-6	-1+(-6)=-7
-2	-3	-2+(-3)=-5

From this list we can see that 2 and 3 add up to 5 and multiply to 6

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

Looking at the factorization, the terms and are the factors of the polynomial .

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