document.write( "Question 957948: find a polynomial of degree 4 that has the following zeros -3i, 3i, -2 multiplicity of two
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Algebra.Com's Answer #585467 by jsmallt9(3758) $\"\"$ $\"About$

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If z is a zero of a polynomial then (x-z) is a factor of that polynomial. And if the multiplicity of a zero is more than 1, then (x-z) is a factor as many times as the multiplicity.

\n" ); document.write( "So if -3i, 3i and -2 with a multiplicty of 2 are zeros then
\n" ); document.write( "(x - (-3i)) or (x + 3i) is a factor
\n" ); document.write( "(x - 3i) is a factor
\n" ); document.write( "(x - (-2)) or (x + 2) is a factor twice.

\n" ); document.write( "To find the polynomial, just multiply all the factors:
\n" ); document.write( "(x + 3i)*(x - 3i)*(x + 2)*(x + 2)
\n" ); document.write( "Hint: The multiplication will be easier if you...

Use the $\"%28a%2Bb%29%28a-b%29+=+a%5E2-b%5E2\"$ pattern to multiply (x + 3i)*(x - 3i). (Remember to replace $\"i%5E2\"$ with -1.)
Use the $\"%28a%2Bb%29%28a%2Bb%29+=+a%5E2%2B2ab%2Bb%5E2\"$ to multiply (x + 2)*(x + 2).
Then multiply the results of the first two multiplcations.

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