function

posted by .

given that f(x)= 3-7x+5x^2-x^3, factorise the polynomial completely, hence state the set of values of x for which the function is equal or less than zero .

  • function -

    -1 ( x^3 - 5 x^2 + 7 x - 3)

    I can see right away that x = 1 makes this zero because 8-8 = 0
    divide polynomial by (x-1)
    ******_x^2_-_4x____+_3_______________
    x-1 / x^3 - 5 x^2 + 7 x - 3
    *******x^3 - 1 x^2
    *******---------------------
    ***********- 4 x^2 + 7 x -3
    ***********- 4 x^2 + 4 x
    ***********-----------------
    *******************+ 3 x - 3
    *******************+ 3 x - 3
    remainder =0
    so
    -1 (x-1)(x^2 - 4 x + 3)
    so
    -1 (x-1)(x-1)(x-3)
    zeros at 1, 1 (double,just hits axis) and 3
    graph it remembering the - sign

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. domain

    Find the domains of f and f' 1, f(x) = xe^x 2. f(x) = x^(3/5) 3. f(x) = x/(x-2) TIA 1) R 2) It's the interfal from zero to infinity for f but for f' it is this inteval with zero excluded, because unlike f, f' is singular at zero. 3) …
  2. Pre-Calculus

    Given that x is an integer, state the relation represented by absolute value y = x/2 and 0 is less than or equal to x which is less than or equal to 2 by listing a set of ordered pairs. Then state whether the relation is a function. …
  3. Math 116

    Use all available methods (in particular, the Conjugate Roots Theorm if applicable) to factor the polynomial function completely, making use of the given zero, f(x)=x^4+x^3+4x^2+196x-2205; -7i is a zero.
  4. Calculus

    Consider the function f(x)=6x-cos(x)+5 on the interval 0 is less than or equal to x, and x is less than or equal to 1. The Intermediate Value Theorem guarantees that there is a value c such that f(c)=k for which values of c and k?
  5. calculus

    Consider the function f(x)=65x−cos(x)+2 on the interval 0 less than or equal to x less than or equal to 1. The Intermediate Value Theorem guarantees that there is a value c such that f(c)=k for which values of c and k?
  6. Calculus c

    Let f be a twice-differentiable function defined on the interval -1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the x-axis at …
  7. Calculus

    Let f be a twice-differentiable function defined on the interval -1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the x-axis at …
  8. maths

    Given the identity x^4-2x^3+ax^2-2=x(x-1)(x+1)Q(x)+4x^2+bx+c , where Q(x)is a polynomial, (i)state the degree of Q(x) (ii)find the values of a,b and c ,and hence state the remainder when x^4-2x^3+ax^2-2 is divided by x^3-x .
  9. maths

    When the function f(x) is equal to 2xn + ax2 - 6 is divided by (x-1), the reminder is -7 and when divided by (x+3), the reminder is 129. Calculate the value of "a" and "n" and hence write the polynomial function completely.
  10. calculus 1

    f(x) = 3x^3 - 9x + 5 find the: 1) zeroes or undefined values 2) intervals where the function is greater than zero 3) intervals where the function is less than zero 4) coordinates of all maxima and minima 5) intervals where the function …

More Similar Questions