Find a degree 3 polynomial having zeros -1, 3 and 7 and the coefficient of x 3 equal 1. The polynomial is

Answer 1

x =-1

x+1 = 0 is one factor

x=3

x-3 = 0 is another factor

x= 7

x-7 = 0 is a 3rd factor

multiply the 3 factors together and expand to get the 3rd degree polynomial

take each zero and change its sign, then stick an x in front of it, then multiply them all together

(x+1)(x-3)(x-7)

= (x^2 -2x -3)(x-7)

= x^3 -2x^2 -3x -7x^2 +14x + 21

= x^3 - 9x^2 + 11x + 21 (the x^3 term has an implicit coefficient of 1. (1)x^3 = x^3)

check the answer by plugging in each zero and see if the polynomial = 0

(-1)^3 -9(-1)^2 +11(-1) + 21 = -1-9-11 + 21 = 0

(3)^3 -9(3)^2 + 11(3) + 21 = 27 -81 +33 +21 = 0

(7)^3 -9(7)^2 +11(7) + 21 = 346 - 441 +77 +21 = 0