Challenging math questions involving polynomial functions
2005年9月18日 · 2. If 2x^3 - 9x^2 + 13x + k is divisible by x - 2, then it is also divisible by x -1. 8. An unknown polynomial f (x) of degree 37 yields a remainder of 1 when divided by x - 1, a remainder of 3 when divided by x - 3, a remainder of 21 when divided by x - 5. 9. If ax^3 + bx + c, with a not equal 0, c not equal 0, has a factor of the form x^2 ...
What's the difference between polynomials and polynomial …
2010年11月10日 · Science Advisor. 1,866. 34. There is just a technical difference, a polynomial function has a domain and co-domain associated to it, whereas a polynomial in a polynomial ring does not. A polynomial in may be viewed as a function from the integers, rationals, reals, complex numbers, real nxn matrices, function spaces, sequence spaces or anything ...
Vector Spaces and polynomial functions - Physics Forums
2004年2月7日 · The operations of polynomial addition and scalar multiplication follow the same rules as vector addition and scalar multiplication, making polynomial functions a type of vector in their own right. Additionally, the set of all polynomial functions with coefficients from a certain field (such as real numbers) can form a vector space.
Precalculus: Writing polynomial functions (help) - Physics Forums
2006年9月26日 · Functions Polynomial Precalculus Writing In summary, the conversation discusses finding a polynomial function with real coefficients and minimum degree that has -1 and 1+4i as zeros. After some discussion and trial and error, it is determined that the polynomial must have a degree of at least 4 and its factors are x+1, x-1-4i, and x-1+4i.
Do polynomials have asymptotes? - Physics Forums
2006年4月7日 · Yes, a polynomial can have multiple asymptotes. For example, a rational function with a numerator of degree 2 and a denominator of degree 3 will have two vertical asymptotes and one horizontal asymptote. The number of asymptotes will depend on the degree and factors of the polynomial.
Finding the Inverse of Cubic Functions - Physics Forums
2004年10月11日 · To find the inverse of a cubic function, you can follow these steps:1. Write the original function in the form f (x) = ax^3 + bx^2 + cx + d.2. Replace f (x) with y.3. Switch the x and y variables so that the equation becomes x = ay^3 + by^2 + cy + d.4. Solve for y using algebraic methods.5. Replace y with f^-1 (x) to represent the inverse function.
Is this business graph an exponential or polynomial function?
2021年8月31日 · The best way to determine if a business graph represents an exponential or polynomial function is to look at the shape of the graph. Exponential functions will have a curved, J-shaped graph, while polynomial functions will have a more linear, U-shaped graph. 3.
2008年3月3日 · Parametric Cubic Spline Tutorial. Parametric equations are powerful and flexible. Perhaps the most familiar example is the equation of a circle in the form x = r*cos(θ), y = r*sin(θ). In this case, the parameter θ is the independent variable and increases monotonically (i.e. each successive value is larger than the previous one, which is a ...
Prove that an even degree poly has either a absolute max or min.
2010年11月16日 · Absolute Degree even Max. In summary, the conversation discusses a problem that states an even degree polynomial has either an absolute max or min. The individual provides a proof using Bolzano-Weierstrass, completeness, and at least 2 limit theorems. Another individual suggests a simpler proof using the extreme value theorem on a closed interval.
Determining the least possible degree of a polynomial function
2013年10月8日 · To determine the least possible degree of a polynomial function, you must first simplify the function by combining like terms and eliminating any unnecessary terms. Then, count the number of variables and exponents present in the simplified function. The least possible degree is the lowest number of variables and exponents present in the ...