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What are quadratic polynomial quartic polynomial constant polynomial and quintic polynomial?
Those words refer to the degree, or highest exponent that modifies a variable, or the polynomial.
Constant=No variables in the polynomial
Linear=Variable raised to the first power
Quadratic=Variable raised to the second power (or "squared")
Cubic=Variable raised to the third power (or "cubed")
Quartic=Variable raised to the fourth power
Quintic=Variable raised to the fifth power
Anything higher than that is known as a "6th-degree" polynomial, or "21st-degree" polynomial. It all depends on the highest exponent in the polynomial. Remember, exponents modifying a constant (normal number) do not count.
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Classification of polynomial according to the number of terms?
Polynomials can be classified based on the number of terms they contain. A polynomial with one term is called a monomial, such as 5x or -2y^2. A polynomial with two terms is called a binomial, like 3x + 2 or 4y - 7. A polynomial with three terms is called a trinomial, for example, 2x^2 + 5x - 3. Polynomials with more than three terms are simply referred to as polynomials.
What is a polynomial with four terms?
First off, it is NOT A QUINTIC! Typically a polynomial of four or more terms is called "a polynomial of n terms", where n is the number of terms. Only the one, two, and three term polynomials are referred to by a particular naming convention.
Determine the maximum or minimum value of y-3x2 12x-7 by completing the square?
Every polynomial defines a function, often called P. Linear and and quadratic function belong to a family of functions known as polynomial functions, which often are called P(x). When P(x) = 0, we call it an equation. Any value of x for which P(x) = 0 is a root of the equation and a zero of the function. Polynomials of the first few degrees have a special names such as:Degree 0: Constant functionDegree 1: Linear functionDegree 2: Quadratic functionDegree 3: Cubic functionDegree 4: Quartic functionDegree 5: Quintic functionSo, if we work a little bit to the given expression, we can turn it in a polynomial function of the second degree.y - 3x^2 = 12x - 7y - 3x^2 + 3x^2 = 12x - 7 + 3x^2y = 3x^2 + 12x - 7Let's write y = f(x) and f(x) = 3x^2 + 12x - 7, where a = 3, b = 12, and c = -7.Since a > 0, the parabola opens upward, so we have a minimum value of the function. The maximum or minimum value of the quadratic function occurs at x = -(b/2a).x = -12/6 = -2To find the minimum value of the function, which is also the y-value, we will find f(-2).f(-2) = 3(-2)^2 + 12(-2) - 7f(-2) = 12 - 24 - 7 = -19Thus the minimum value of the function is -19, and the vertex is (-2, -19)To find zeros, we solve f(x) = 0. So,f(x) = 3x^2 + 12x - 7f(x) = 03x^2 + 12x - 7 = 0 In order to solve this equation by completing the square, we need the constant term on the right hand side;3x^2 + 12x = 7 Add the square of one half of the coefficient of x to both sides, (6^2)3x^2 +12x + 36 = 7 + 36 Use the formula (a + b)^2 = a^2 + 2ab + b^2;(3x + 6)^2 = 43 Take the square root of both sides, and solve for x;3x + 6 = (+ & -)square root of 433x + 6 = (+ & -)(square root of 43) Subtract 6 to both sides;3x = (+ & -)(square root of 43) - 6 Divide both sides by 3;x = (square root of 43)/3 - 2 or x = -(square root of 43)/3 - 2The solution are (square root of 43) - 2 and -(square root of 43) - 2
What is this pattern rule for this pattern 21-66-42-61-84-56?
The numbers fit the quintic function: t(n) = (27n5 - 556n4 + 4253n3 - 14876n2 + 23440n - 11784)/24 for n = 1, 2, 3, etc
