Need help with homework please show work Find a polynomial f

Find a polynomial function of degree three with numbers 3,5, -2 as zeros of the polynomial. Q2. Consider the quadratic model h(t) = -16t^2 + 40t + 50 for the height (in feet), h, of an object t seconds after the object has been projected straight up into the air. a) Find the maximum height attained by the object. Use the vertex formula. b) How much time does it take to fall back to die ground? Assume that it takes the same time for going up and coming down. Q3. Find the rational zeros of the function f(x) = x^4 -6X^3 +9x^2 +6x-10. Then, factor f(x) into linear factors. Q4. Find a polynomial function of lowest degree with real coefficients and the numbers 6, 3i as some of its zeros. Q5. Perform the long division of potoomials to find the quotient and remamder when dividing x^4 + 3x^3 + 3x^2 + 3x + 2 by x + 2.

Solution

1) Zero of 3 means: (x-3)=0   ____(1)

Zero of 5 means: (x-5)=0   ____(2)

Zero of -2 means: (x+2)=0   ____(3)

Comining (1), (2) & (3)

(x-3)(x-5)(x+2) = 0

=> (x² - 3x - 5x + 15)(x+2) = 0

=> (x² -8x +15)(x+2) = 0

=> x³ +2x² - 8x² -16x + 15x + 30 = 0

=> x³ - 6x² - x + 30 = 0