Question 1011139
Real roots are -5 and -2;
Other complex roots are  -2+2i, -2-2i, -4-2i, -4+2i.
Further, {{{f(x)=a*(polynomialDegree6)}}} and you use the y-intercept to finally find a.


Start with {{{f(x)=a(x+5)(x+2)(x-(-2+2i))(x-(-2-2i))(x-(-4-2i))(x-(-4+2i))}}}.


{{{a(x+5)(x+2)(x+2-2i)(x+2+2i)(x+4+2i)(x+4-2i)}}}


{{{a(x+5)(x+2)((x+2)^2+4)((x+4)^2+4)}}}----this really combined two steps including knowing about difference of squares and of i*i=-1;


{{{a(x+5)(x+2)(x^2+4x+4+4)(x^2+8x+16+4)}}}


{{{a(x+5)(x+2)(x^2+4x+8)(x^2+8x+20)}}}--------at this stage, the function is in purely factored form without showing complex nor imaginary expressions - only real coefficients.  You CAN still use this to find the value for a, making use of the given y-intercept; and you may still want to continue the full multiplication into general form.