polynomial

  1. O

    Identifying polynomial variables

    Hi, I hope someone can help. I'm trying to solve for the following problem: So far I have identified the value for c, which is 1. And then I plugged in the points (3,12) in order to isolate a and b. As follows: I'm struggling to solve for a and b. When I sub a into b, or visa versa, I...
  2. R

    Find zeros of cubic polynomial without a constant term

    Hi, Could someone assist with this problem. F(x)=5x-x^3 Here is what I did: -x(x^2+5) I tried synthetic division using +-1, +-5, with no luck. Thanks. RB
  3. N

    Polynomial f(x) such that f(x)f(1/x)=f(x)+f(1/x)

    My teacher said that the polynomial function such that f(x)f\left(\frac{1}{x}\right)=f\left(x \right )+f\left(\frac{1}{x} \right ) exists and that must be of the form f(x)=1 \pm x^n. But he didnt give any proof. Can anyone help me with a proof that the function satisfying the above condition can...
  4. O

    Rates of Change for Rational Functions

    Hi, I hope someone can help. I'm currently trying to answer homework question 12a: I can't seem to be getting the correct answer - which according to my textbook is 0.01. Here are my calculations...
  5. O

    Understanding oblique asymptotes

    Hi, I hope someone can help. I'm confused about the definition for oblique asymptotes. Do oblique asymptotes only exist when the numerator is exactly one degree larger than the denominator? What do you call something which has a numerator that is more than one degree larger than the...
  6. O

    Rational functions in the context of polynomials

    Hi, I want someone to confirm whether or not I'm right about my thinking in terms of rational and polynomial functions. I know that one main feature of polynomial functions is that it can't have division by a variable. So would this suggest that rational functions are not considered...
  7. O

    Reciprocal functions

    Hi, I hope someone can help. Remember that vertex form is y = a(x-h)^2+k I'm trying to understand why the function f(x) = 3x^2-4x-4 in vertex form is f(x) = (x-2/3)^2 - 16/9. Really what I'm wondering is why would k = -16/9 given that the vertex has a y-value of -5.3? I always was taught...
  8. O

    Transformation of a polynomial function

    Hi, I hope someone can help. So I developed a polynomial function: f(x) = 1/9(x+3)(x+1)(x-3)(x-1) I am now trying to horizontally compress this function by a factor of 2. Can someone please confirm with me that the new equation with this transformation applied is f(x) =...
  9. J

    4th Degree Polynomial

    How to factor this function? y = x^4 + x^2 + 2
  10. O

    Instantaneous rate of change: determining where it is positive, negative, and zero

    Hi, I hope someone can help. I'm trying to find the x-coordinate for the turning point (circled in red) within my drawing: This drawing is based on the equation f(x) = x^3-2x^2+x I need to know this x-coordinate in order for me to accurately state the intervals where the rate of change is...
  11. O

    Average rate of change

    Hi, I hope someone can help. I'm trying to solve for 4a: The answer is apparently 7 - however I don't understand how there could even be an average rate of change that has no slope to begin with. y = f(x) is a horizontal line, therefore there is no slope. Please let me know if my thinking is...
  12. O

    Instantaneous rate of change

    Hi, I hope someone can help. I'm trying to understand why my solution is wrong for 3a: I don't understand why the solution is zero given that the slope at x = 2 produces non-zero numbers. Maybe I'm just calculating it incorrectly. Can someone provide me with the rights steps to solve this...
  13. O

    Polynomial inequality - word problem

    Hi, I hope someone can help. I'm trying to solve for the following question: <= "less than or equal to" >= "greater than or equal to" These are my steps: 1. I know that the volume of a rectangle is l x w x h - therefore the inequality to the equation must be x(50 - 2x)(30 - 2x) <= 4000...
  14. O

    Polynomial inequality

    Hi, I hope someone can help. I'm trying to solve 11b and 11c: For 11b - I don't understand why the solution is only 0 < 154.75 Celsius. I see other parts of this graph where v > 0, namely on the left-hand side of the y-axis, so I'm curious why this is not included in the solution. For...
  15. O

    Projectile problem - finding the roots

    Hi, I hope someone can help. I'm currently doing advanced functions, and I have been presented with a physics-related question that I don't know how to solve. I attached the question in this post: I understand that I have to solve for t. In order to do that, I must know what the acceleration...
  16. O

    Creating equation from graph

    Hi, I hope someone can help. I'm trying to understand how a given equation matches the following function characteristics: The equations are: I understand that the function needs to have an odd degree, one zero at x = 2 that has a multiplicity of 2 (in order for it to "bounce back" and...
  17. O

    Prove that a binomial is a factor

    Hi, I hope someone can help. I'm suppose to prove that x + a is a factor of (x + a)^5 + (x - c)^5 + (a - c)^5. The textbook solution is if f(x) = (x + a)^5 + (x - c)^5 + (a - c)^5, then f(-a) = 0. I don't totally understand this solution, so could someone please elaborate on this? Best, Olivia
  18. O

    Proving a factor of a polynomial

    Hi, I hope someone can help provide elaboration on the homework question that I'm faced with, and why the solution is what it is. The homework question is as follows: Determine a general rules to help decide whether x - a and x + a are factors of x^n - a^n and x^n + a^n. The homework...
  19. O

    Factoring a cubic function

    Hi, I hope someone can help. I'm trying to factor a cubic function, but it appears that I'm doing incorrectly based on my textbook's answer. I attached my steps in this post, along with also the textbook answer. Please let me know where I went wrong in my steps. Sincerely, Olivia My steps...
  20. O

    Polynomial Remainder Theorem

    Hi, I hope someone can provide me with some clarification. I'm trying to find the remainder for a dividend of x^2+9x-7. I already have information regarding the quotient and divisor: (x + 3) and (x + 5). It's unknown which one is the quotient or divisor, but I don't think that's relevant...