Given P(x)=3x^5+10x^4+84x^3+252x^2+225x+50, and that 5i is a zero, write P in factored form (as a product of linear factors). Be sure to write the full equation, including P(x)=.

Question

Given , and that  is a zero, write  in factored form (as a product of linear factors). Be sure to write the full equation, including .

Answer 1

Last week someone submitted this question which I answered.

"Since we have computers which will divide a polynomial by a binomial, why should we learn how to do that long division by hand?"

My answer included the statement that I did not believe students should do onerous work but they should learn how to do the process.

The answer to this problem is as follows:

(x-5i) and (x+5i) are roots, therefore (x² + 25) is a factor.

You are now required to divide (x² + 25) into the polynomial given above; the quotient will be a cubic polynomial which you will then need to factor. You will then have your answer.