SOLUTION: 64x^3+343 x^4+8x^2-9 these are the two polynomials im left with! pleasee help! thankss!

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Question 133352: 64x^3+343
x^4+8x^2-9
these are the two polynomials im left with!
pleasee help!
thankss!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Do you want to factor?

# 1

64x%5E3%2B343 Start with the given expression.


%284x%29%5E3%2B%287%29%5E3 Rewrite 64x%5E3 as %284x%29%5E3. Rewrite 343 as %287%29%5E3.


%284x%2B7%29%28%284x%29%5E2-%284x%29%287%29%2B%287%29%5E2%29 Now factor by using the sum of cubes formula. Remember the sum of cubes formula is A%5E3%2BB%5E3=%28A%2BB%29%28A%5E2-AB%2BB%5E2%29


%284x%2B7%29%2816x%5E2-28x%2B49%29 Multiply

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Answer:

So 64x%5E3%2B343 factors to %284x%2B7%29%2816x%5E2-28x%2B49%29.

In other words, 64x%5E3%2B343=%284x%2B7%29%2816x%5E2-28x%2B49%29







# 2


Looking at 1x%5E4%2B8x%5E2-9 we can see that the first term is 1x%5E4 and the last term is -9 where the coefficients are 1 and -9 respectively.

Now multiply the first coefficient 1 and the last coefficient -9 to get -9. Now what two numbers multiply to -9 and add to the middle coefficient 8? Let's list all of the factors of -9:



Factors of -9:
1,3

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

These factors pair up and multiply to -9
(1)*(-9)
(-1)*(9)

note: remember, the product of a negative and a positive number is a negative number


Now which of these pairs add to 8? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 8

First NumberSecond NumberSum
1-91+(-9)=-8
-19-1+9=8



From this list we can see that -1 and 9 add up to 8 and multiply to -9


Now looking at the expression 1x%5E4%2B8x%5E2-9, replace 8x%5E2 with -1x%5E2%2B9x%5E2 (notice -1x%5E2%2B9x%5E2 adds up to 8x%5E2. So it is equivalent to 8x%5E2)

1x%5E4%2Bhighlight%28-1x%5E2%2B9x%5E2%29%2B-9


Now let's factor 1x%5E4-1x%5E2%2B9x%5E2-9 by grouping:


%281x%5E4-1x%5E2%29%2B%289x%5E2-9%29 Group like terms


x%5E2%28x%5E2-1%29%2B9%28x%5E2-1%29 Factor out the GCF of x%5E2 out of the first group. Factor out the GCF of 9 out of the second group


%28x%5E2%2B9%29%28x%5E2-1%29 Since we have a common term of x%5E2-1, we can combine like terms

So 1x%5E4-1x%5E2%2B9x%5E2-9 factors to %28x%5E2%2B9%29%28x%5E2-1%29


So this also means that 1x%5E4%2B8x%5E2-9 factors to %28x%5E2%2B9%29%28x%5E2-1%29 (since 1x%5E4%2B8x%5E2-9 is equivalent to 1x%5E4-1x%5E2%2B9x%5E2-9)





So x%5E4%2B8x%5E2-9 factors to %28x%5E2%2B9%29%28x%5E2-1%29


%28x%5E2%2B9%29%28x%2B1%29%28x-1%29 Now factor x%5E2-1 by using the difference of squares
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Answer:


So x%5E4%2B8x%5E2-9 factors to %28x%5E2%2B9%29%28x%2B1%29%28x-1%29