Given a polynomial that has zeros of -3,9i, and -9i and has a value of 255 when x=−2. Write the polynomial in standard form Axn+ban−1... Answer using the reduced fractions when necessary.

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Melinda Olson · Accepted Answer

Step 1Given:Zeros of the polynomial are -3, 9i, -9iStep 2If x=a is the zero of the given polynomial then (x−a) is the factor of that polynomial.Given zeros are x=−1,x=9i,x=−9iTherefore factor&#039;s are (x+1),(x−9i),(x+9i)Now find the polynomial using the factors consider leading coefficient is af(x)=a(x+1)(x−9i)(x+9i)f(x)=a(x+1)(x2−9ix+9ix−81(i)2)f(x)=a(x+1)(x2+81)f(x)=a(x3+x2+81x+81)To find a use given condition x=−2,f(x)=255f(−2)=a((−2)3+(−2)2+81(−2)+81)255=a(−8+4−162+81)255=a(−85)a=−25585a=−5117Step 3f(x)=−5117(x3+x2+81x+81)f(x)=−5117x3−5117x2−243x−243Step 4Answer:f(x)=−5117x3−5117x2−243x−243 orf(x)=−(5117x3+5117x2+243x+243)

Given a polynomial that has zeros of -3,9i, and -9i and has a value of

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