find a polynomial with single roots at x=5 and x=-1 and a double root at x=1 in standard form

Question

any help would be greatly apprecaited

Answer 1

Hope this helps.

Four roots have been defined making factors (x+1)(x-5)(x-1)^2.

Expanding: (x^2-4x-5)(x^2-2x+1)=x^4-2x^3+x^2 - 4x^3+8x^2-4x - 5x^2+10x-5.

Grouping similar terms: x^4-6x^3+4x^2+6x-5.