Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Fourth-degree and a single zero of −3.

Answer 1

x=-3

x+3 = 0

f(x) = (x+3)^4 just one zero with multiplicity 4 is a polynomial function with degree 4

if you want you can multiply it out

(x+3)^4 = (x+3)^2(x+3)^2 = (x^2 +6x + 9)(x^2 +6x +9) = x^4 +12x^3 + 54x^2 + 108x + 81

Pascal's Triangle helps give the coefficient. x terms reduce their exponents by 1 in descending order

3x4 =12 for the x^3 coefficient

3^2 x 6 = 54 for the x^2 coefficient

3^3 x 4= 27x4 = 108 for the x coefficient

3^4 = 81 for the constant term

1

11

121

1331

14641