How do you find a polynomial function that has zeros 4, -3, 3, 0? Precalculus Polynomial Functions of Higher Degree Zeros 1 Answer Alan N. Mar 9, 2017 #f(x) = x^4-4x^3-9x^2+36x# Explanation: If #f(x)# has zeros of #4, -3, 3, 0 -> (x-4), (x+3), (x-3), x# are factors of #f(x)# Hence: #f(x) = (x-4)(x+3)(x-3)x# #f(x) = x(x-4)(x^2-9)# #= (x^2-4x)(x^2-9)# # = x^4-4x^3-9x^2+36x# Answer link Related questions What is a zero of a function? How do I find the real zeros of a function? How do I find the real zeros of a function on a calculator? What do the zeros of a function represent? What are the zeros of #f(x) = 5x^7 − x + 216#? What are the zeros of #f(x)= −4x^5 + 3#? How many times does #f(x)= 6x^11 - 3x^5 + 2# intersect the x-axis? What are the real zeros of #f(x) = 3x^6 + 1#? How do you find the roots for #4x^4-26x^3+50x^2-52x+84=0#? What are the intercepts for the graphs of the equation #y=(x^2-49)/(7x^4)#? See all questions in Zeros Impact of this question 6090 views around the world You can reuse this answer Creative Commons License