How can i rewrite x^3-3x^2+81x-243 in the form of (x-d)(x-e)(x+f) where d is a real number and e and f are complex numbers of the form bi?

If is a polynomial of degree and are his roots, we can write

So, the exercise is basically asking you to find the three roots of the polynomial.

Cubic polynomials don't have a closed formula to solve them (well, they have, but it's very complicated), so we'd better use the rational root theorem.

This theorem states that the possible rational solutions of a polynomial with integer coefficients are of the form , where p is a divisor of the known term, and q is a divisor of the leading term.

So, in our case, we have to try all the divisors of 243 (with both signs). We find out that

So, x=3 is a solutions, and we can write as

And we can find the remaining polynomial by writing

The solutions of this polynomial are

This means that the solutions of are , ,

So, we can factor it as

step-by-step explanation: yes

answer: a. 13/44

step-by-step explanation: judging by the information given to us, we are looking for experimental probability. we can see that 13 males have chosen chocolate ice cream. there are 44 ice creams in total (remember that the total is always the denominator). so our answer is 13/44.