Q22 Find all zeros of the function fx 2x4 3x3 16x2 27x

Q22. Find all zeros of the function f(x) = 2x⁴ + 3x³ + 16x² + 27x - 18 and write the polynomial as a product of linear factors.
    a. f(x) = (2x - 1)(x + 2)(x + 3)(x - 3)
    b. f(x) = (2x + 1)(x - 2)(x + 3)(x - 3)
    c. f(x) = (2x - 1)(x + 2)(x + 3i)(x - 3i)
    d. f(x) = (2x + 1)(x - 2)(x + 3i)(x - 3i)

Q23. Find the x-intercepts of the graph of the function f(x) = (x - 3)(2x + 7)/(x² + 9x - 8).
    a. (3, 0), (-7, 0)
    b. (-3, 0), (7/2, 0)
    c. (3, 0), (-7/2, 0)
    d. none

Q26. Find the domain of the rational function f(x) = (x + 9)/(x² - 4x).
    a. {x|x -2, x 2}
    b. {x|x -2, x 2, x -9}
    c. all real numbers
    d. {x|x 0, x 4}

24 and 25 I already answered I was just curious if they are right.

Solution

22. the polynomial 2x4 + 3x3 + 16x2 + 27x - 18 can be factorized to = (2x - 1)(x + 2)(x + 3i)(x - 3i)

23. to find the x intercepts put f(x) = 0

then we get (x-3)(2x+7) = 0

so we get y = f(x) is 0 when x-3 = 0 or x=3 and 2x+7 = 0 or x = -7/2

(-3,0) , (-7/2,0)

26. The denominator is x(x-4) so the finction is not defined when x = 0 and x = 4

so answer is d. {x|x 0, x 4}

24 is correct but 25 is not a . the function valuesa are always positive. so since we are doing 5 times x^{4 .} The graph of the function becomes bit more steeper. i think it should be probably d (You have not gven the figure)