X 4 13x 2 36

Institute 3 solutions by jim_thompson5910, Alan3354, ankor@dixie-net.com:

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Answer by jim_thompson5910(35256) (Show Source):

You lot can put this solution on YOUR website!

Looking at we can come across that the start term is and the concluding term is where the coefficients are 1 and 36 respectively.

Now multiply the kickoff coefficient i and the last coefficient 36 to go 36. Now what ii numbers multiply to 36 and add together to the center coefficient -xiii? Let'southward list all of the factors of 36:

Factors of 36:
1,2,3,4,6,9,12,18

-one,-ii,-3,-four,-6,-nine,-12,-xviii ...List the negative factors equally well. This will allow united states to find all possible combinations

These factors pair upwards and multiply to 36
i*36
two*18
iii*12
4*9
6*half dozen
(-1)*(-36)
(-two)*(-18)
(-three)*(-12)
(-iv)*(-ix)
(-6)*(-6)

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

At present which of these pairs add to -13? Lets make a table of all of the pairs of factors we multiplied and run into which two numbers add together to -13

First Number	Second Number	Sum
i	36	i+36=37
ii	18	2+eighteen=20
3	12	3+12=15
4	ix	4+9=13
6	6	6+6=12
-1	-36	-1+(-36)=-37
-two	-18	-2+(-18)=-20
-iii	-12	-3+(-12)=-15
-4	-nine	-4+(-ix)=-13
-half-dozen	-vi	-6+(-half-dozen)=-12

From this list we can see that -iv and -9 add up to -13 and multiply to 36

At present looking at the expression , supervene upon with (notice adds upwardly to . And then it is equivalent to )

Now let'due south factor by grouping:

Grouping like terms

Factor out the GCF of out of the first grouping. Factor out the GCF of out of the 2d group

Since nosotros take a common term of , we tin can combine like terms

So factors to

So this also means that factors to (since is equivalent to )

So factors to

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Showtime with the given factorization

Factor to get (by use of the divergence of squares)

Gene to go (by use of the difference of squares)

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Reply:

Then completely factors to

Note: the order of the factors does not matter.

Answer by Alan3354(68915) (Testify Source):

You can put this solution on YOUR website!
Factor....Need some help
x^four-13x^ii+36
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Information technology volition exist (x^2 + ?)*(x^2 + ?)
The ?'s production will exist 36, and they add upward to -13.
Since it's +36, they have to have the same sign, both Pos or both Neg.
Since they add to -thirteen, they'll have to be both negative.
Consider the factors of 36:
1*36
2*eighteen
iii*12
four*9, and
six*6
They're the same sign, so that add to thirteen. If the were not the same sign, you would look at the differences.
Only 4 and 9 add to 13, so they're it.
It's (10^ii - 4)*(x^2 - ix)

Answer by ankor@dixie-net.com(22666) (Testify Source):

You can put this solution on YOUR website!
x^4 - 13x^two + 36
Factor this similar an ordinary quadratic except yous have:
:
(x^2 - 9)(x^two - iv); (If yous FOIL this you will get the original expression)
:
Note that each factor is the "difference of squares" and can be further factored
(ten^2 - 9) = (10 - iii)(x + 3)
and
(x^2 - 4) = (ten - 2)(ten + 2)

X 4 13x 2 36,

Source: https://www.algebra.com/algebra/homework/Distributive-associative-commutative-properties/Distributive-associative-commutative-properties.faq.question.168695.html

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