Form a polynomial whose real zeros and degree are given

Question

Form a polynomial whose real zeros and degree are given.

Zeros: -3,-1,2,4

degree:4

type a polynomial with integer coefficients and a leading coefficient of 1.

Answer 1

since the zeros are -3,-1,2,4 we know we have the factors,

(x+3) (x+1) (x-2) (x-4)

multiplying these factors together will give a 4th degree polynomial with leading coefficient 1 and integer coefficients

(x+3)(x+1)(x-2)(x-4)

= (x²+4x+3)(x²-6x+8)

= x²(x²-6x+8)+4x(x²-6x+8)+3(x²-6x+8)

= x⁴-2x³-13x²+14x+24