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 ) }}

Algebra ->  Polynomials-and-rational-expressions -> 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 ) }}      Log On


   

Question 382648: i am confused on how to answer the following questions.
factor completely: %282a+%2B+b%29%5E3+-+b%5E3+
and
Write a polynomial function that has zeros 0, 1,+3+-+sqrt%28+5+%29+
Found 2 solutions by kingme18, solver91311:
Answer by kingme18(98) About Me  (Show Source):
You can put this solution on YOUR website!
The first problem is a difference of two cubes.
The formula for this is x%5E3+-+y%5E3=%28x-y%29%28x%5E2%2Bxy%2By%5E2%29
For your problem, 2a+b will be used in place of x, and b will be used in place of y.
%28%282a%2Bb%29-b%29%28%282a%2Bb%29%5E2%2B%282a%2Bb%29b%2Bb%5E2%29
Simplify: %282a%29%284a%5E2%2B4ab%2Bb%5E2%2B2ab%2Bb%5E2%2Bb%5E2%29
Combine like terms: %282a%29%284a%5E2%2B6ab%2B3b%5E2%29
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 x=3-sqrt%285%29. For each of these, get everything to the same side so that each one equals 0. x=0, x-1=0, and x-3%2Bsqrt%285%29=0. The polynomial function is the product of these: f%28x%29=x%2A%28x-1%29%2A%28x-3%2Bsqrt%285%29%29. You can multiply this out to make it look more like a typical polynomial.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


You have the difference of two cubes.



Let and let

Then just substitute into the pattern:



Of course there is still a lot of simplification to do. I'll leave that as an exercise for the student.

John

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