determine the polynomial P(x) of lowest degree that has these properties: a roof of -1 with multiplicity 2, a root of 2-square root 3 and P(1)=32

Find a formula for the polynomial of least degree that is graphed below.

Consider the following higher degree polynomial function f(x) = -2x² (5-2x) (x² + 1). a) What is the degree of this function? b) How many zeros does this function have? c) State the coordinates of the y-intercept.

What is the maximum number of zeros (x-intercepts) that a polynomial of degree 12 can have?

The function, f(x) =x³ + x² – 13x + 3 has an x-intercept at x = 3. Use polynomial division to factor this polynomial and determine the other roots if they exist. Show your work! Leave answer(s) in exact form.

Write a polynomial f(x) that satisfies the given conditions. Polynomial of lowest degree with real coefficients and with zeros 7-4i and 0(multiplicity 4). The answer is f(x)= x^6-14x^5+65x^4. If possible, please give step-by-step solutions. Thank you, and God bless.

find the maximum number of real zeroes of the polynomial  f(x)=-2x7-3x8-6-5x5

find all the roots for the following polynomial and give the multiplicity for each root 2x6 (x-9) (x+5)2 (x-3)4 (x+5) (x-3)

What is the maximum number of real roots a 5th-degree polynomial can have?

What is the polynomial function in standard form with a root of multiplicity 1 at x = 3, and a root of multiplicity 2 at x = 4? Show all work.