SOLUTION: i am confused on how to answer the following questions.
factor completely: {{{(2a + b)^3 - b^3 }}}
and
Write a polynomial function that has zeros 0, 1,{{{ 3 - sqrt( 5 ) }}
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Question 382648: i am confused on how to answer the following questions.
factor completely:
and
Write a polynomial function that has zeros 0, 1,
Found 2 solutions by kingme18, solver91311:
Answer by kingme18(98) (Show Source): You can put this solution on YOUR website!
The first problem is a difference of two cubes.
The formula for this is
For your problem, 2a+b will be used in place of x, and b will be used in place of y.
Simplify:
Combine like terms:
That is the final answer :)
For a polynomial to have specific zeros, you'll have to say x = whatever the zero is. Here, x=0, x=1, and . For each of these, get everything to the same side so that each one equals 0. x=0, x-1=0, and . The polynomial function is the product of these: . You can multiply this out to make it look more like a typical polynomial.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You have the difference of two cubes.
(x^2\ +\ xy\ +\ y^2)
Let 
and let 
Then just substitute into the pattern:
^3\ -\ b^3\ =\ (2a\ +\ b\ -\ b)\left((2a\ +\ b)^2\ +\ 2ab\ +\ b^2\ +\ b^2\right))
Of course there is still a lot of simplification to do. I'll leave that as an exercise for the student.
John
My calculator said it, I believe it, that settles it
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