14) A family of cubic polynomials has roots of -2, -3 and -5. Find the member of this family that passes through the point (2,-35). What is this polynomials y-intercept?

Write polynomial functions of minimal degree with the indicated properties.    a) integer coefficients; roots 3 (multiplicity 2) and -1 (multiplicity 3);  y-intercept 18 b) integer coefficients: roots 2, -2,  √2 and -3 ;  contains the point (1,24) c) integer coefficients; roots 1 and 2 + √3;  coefficient is x^3 is 1

3) Assume you have a polynomial of degree 3, P(x), where P(2)=0. Describe how you will find the other zeros of the polynomial.

please refer to the image for the question, thank you!

5x^2-12+30/x^2+2 find f(-4) using the remainder theorem

19) Find the distance between these two points (-8, 5) and (15, -9) Use the formula: d = square root of [(x2– x1)² + (y2 - yı)²]

Find all roots of x^4-7x^3+18x^2-22x+12 fiven that 1-i is a zero and sketch the graph

What are the zeros of the equation y + 4x = x³? (2, 0) (0, -2) (0, 0), (2, 0) and (-2, 0) (0, 2), (-2, 0) and (9, 0) (0, 0), (0, 4) and (0, -4)

Determine the rule for a polynomial function with rational coefficients and least possible degree that has a root at x = 1+√3, another root at x=4-√2, and passes through the point (2,-16).

Find the roots of f(x) = 4x^2 + 8x -7 Find the vertex using the roots (different procedure than regularly finding vertex).