document.write( "Question 382648: i am confused on how to answer the following questions.\r
\n" ); document.write( "\n" ); document.write( "factor completely: $\"%282a+%2B+b%29%5E3+-+b%5E3+\"$ \r
\n" ); document.write( "\n" ); document.write( "and\r
\n" ); document.write( "\n" ); document.write( "Write a polynomial function that has zeros 0, 1, $\"+3+-+sqrt%28+5+%29+\"$ \n" ); document.write( "

Algebra.Com's Answer #271097 by kingme18(98) $\"\"$ $\"About$

You can put this solution on YOUR website!
The first problem is a difference of two cubes.
\n" ); document.write( "The formula for this is $\"x%5E3+-+y%5E3=%28x-y%29%28x%5E2%2Bxy%2By%5E2%29\"$
\n" ); document.write( "For your problem, 2a+b will be used in place of x, and b will be used in place of y.
\n" ); document.write( " $\"%28%282a%2Bb%29-b%29%28%282a%2Bb%29%5E2%2B%282a%2Bb%29b%2Bb%5E2%29\"$
\n" ); document.write( "Simplify: $\"%282a%29%284a%5E2%2B4ab%2Bb%5E2%2B2ab%2Bb%5E2%2Bb%5E2%29\"$
\n" ); document.write( "Combine like terms: $\"%282a%29%284a%5E2%2B6ab%2B3b%5E2%29\"$
\n" ); document.write( "That is the final answer :)
\n" ); document.write( "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. \n" ); document.write( "

\n" );