Polynomial Functions

Question

Please step by step instructions

 

Find all zeros of the function and write the polynomial as a product of linear factors.

f(x) = x4 + 4x3 + 12x2 + 36x + 27

 

 

Thank You :-)

 

Answer 1

 

Hi Bella -- values to try: (+/- factors of the last term) / (+/- factors of the 1st term) ...

 

(+/- 1,3,9,27) / (+/- 1) ... seems -1 and -3 may work ... f(-1) = 1 -4 +12 -36 +27 =0.

f(-3) = 3(27) -4(27) +4(27) -4(27) +27 =0 ... extract (x+1) and (x+3) = x^2 +4x +3.

 

leaves quadratic after f(x) / (x^2 +4x +3) => x^2 +9 ==> imaginary roots of +/- 3i.

 

f(x) = (x+1)(x+3)(x^2 +9) = (x+1)(x+3)(x+ 3i)(x- 3i) ... Best wishes :)