SOLUTION: Make sure to superscript all exponents. If you believe that a polynomial is not factorable, label it as prime, Show all stages of factoring separately(i.e., show the result of fact
Algebra.Com
Question 176141: Make sure to superscript all exponents. If you believe that a polynomial is not factorable, label it as prime, Show all stages of factoring separately(i.e., show the result of factoring out a GCF before taking the resulting polynomial and factoring it again).
2x^3-26x^2+80x
Thanks
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given expression
Factor out the GCF
Now let's focus on the inner expression
------------------------------------------------------------
Looking at we can see that the first term is and the last term is where the coefficients are 1 and 40 respectively.
Now multiply the first coefficient 1 and the last coefficient 40 to get 40. Now what two numbers multiply to 40 and add to the middle coefficient -13? Let's list all of the factors of 40:
Factors of 40:
1,2,4,5,8,10,20,40
-1,-2,-4,-5,-8,-10,-20,-40 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 40
1*40
2*20
4*10
5*8
(-1)*(-40)
(-2)*(-20)
(-4)*(-10)
(-5)*(-8)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to -13? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -13
First Number | Second Number | Sum | 1 | 40 | 1+40=41 |
2 | 20 | 2+20=22 |
4 | 10 | 4+10=14 |
5 | 8 | 5+8=13 |
-1 | -40 | -1+(-40)=-41 |
-2 | -20 | -2+(-20)=-22 |
-4 | -10 | -4+(-10)=-14 |
-5 | -8 | -5+(-8)=-13 |
From this list we can see that -5 and -8 add up to -13 and multiply to 40
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
So this also means that factors to (since is equivalent to )
------------------------------------------------------------
So our expression goes from and factors further to
------------------
Answer:
So completely factors to
RELATED QUESTIONS
Make sure to superscript all exponents. If you believe that a polynomial is not... (answered by Alan3354)
Make sure to superscript all exponents. If you believe that a polynomial is not... (answered by EMStelley)
Make sure to superscript all exponents. If you believe that a polynomial is not... (answered by Earlsdon)
Make sure to superscript all exponents. If you believe that a polynomial is not... (answered by Mathtut)
Make sure to superscript all exponents. If you believe that a polynomial is not... (answered by jim_thompson5910)
Can someone please help me to factor this problem completely
x^3 – 2x^2 + 7x – 14??... (answered by MathLover1)
I am at a loss and do not understand this Factoring. Please help me "Factor Completely"... (answered by ptaylor)
Can someone please help me factor this problem completely?
x^10y^3 - 4x^9y^2 -... (answered by bucky)
If you believe that a polynomial is not factorable, label it as prime.
Factor... (answered by solver91311)