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An expression must have a monomial of degree 2 or higher to be a polynomial?
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∙ 13y ago
False
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∙ 13y ago
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What is A polynomial of degree 1.?
That means that the monomial of the highest degree has a degree higher than 1. For example: x + 5 3x - 7 -27x + 8
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 polynomialLinear=Variable raised to the first powerQuadratic=Variable raised to the second power (or "squared")Cubic=Variable raised to the third power (or "cubed")Quartic=Variable raised to the fourth powerQuintic=Variable raised to the fifth powerAnything 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.
What does polynomial with rational coefficients mean?
Let's define this question one word at a time. A polynomial is an equation with the variable x raised to whole number powers other than 0. This may include 2x + 3, or x2 - 8x + 16, or even x5 - 4x3 + 9. Coefficients are the numbers multiplied by the x term in question. The term 6x3 has a coefficient of 6, the term -x/2 has a coefficient of -1/2 and the term x2 has a coefficient of 1. Rational numbers are those which can be written as a ratio, or a fraction. This means its decimal notation will either have a finite amount of digits, like 0.625 (5/8), or a repeating series of decimals, e.g. 2.16666... or 13/6. Rational numbers can only be formed with addition, subtraction, multiplication and division - this means it excludes functions like taking the square root, the sine, or the log of a number. In summary, a polynomial with rational coefficients is an expression with multiple terms, such as ax2 + bx + c, where the coefficients 'a' and 'b' (and typically 'c' as well, as it is the coefficient of x0 which is 1 by definition, and is therefore being multiplied by 1) are rational numbers. This can extend to mean a polynomial of any degree, be it linear (x), cubic (x3), quartic (x4) or anything higher - so long as the coefficients of all the x terms are rational.
How do you know when a trinomial is factored completely?
When there is no x term with a higher power than 1. Once all x-terms have a power of 1 or below, the expression has been fully factorised.
The expression x to the power of 2 - 2mx has a minimum value as x varies Find the minimum value of x to the power of 2 - 2mx and Give your answer in terms of m?
If this is a homework question, please consider answering it on your own first, otherwise the value of the homework assignment, i.e. to reinforce the lesson, will be lost to you.The minimum or maximum of a function y = f(x) can be found when the deriviative dy/dx f(x), or slope, is zero. In the case of a polynomial of degree two, which this question is, there is only one point where the deriviative is zero. In the general case of a polynomial of degree three or higher, however, any point where the slope is zero might only be a local minimum or maximum, so care must be taken. Also, you must always consider the second deriviative, in order to verify if that point is a minumum or a maximum.The first deriviative of y = x2 - 2mx is 2x - 2m. (Remember, m is constant)By simple algebra, the solution of 2x - 2m = 0 is x = m.To determine if this is a minimum or a maximum, take the second deriviative.The second deriviative of y = x2 - 2mx is the first deriviative of y = 2x - 2m, which is 2.Since 2 is always positive, the slope is always increasing, so the point x = m is a minimum.
True or false An expression must have a monomial of degree 1 or higher to be a polynomial?
False. The height of the degree does not really matter in this case. There just have to be other monomials in the problem to be considered a polynomial. "Poly" means many.
What is A polynomial of degree 1.?
That means that the monomial of the highest degree has a degree higher than 1. For example: x + 5 3x - 7 -27x + 8
What is an example of an expression that is not a polynomial?
A polynomial expression is one with a degree higher than 0. Hence, all constants will meet your criterion. Note that (x+2) or [sin(2x)+4] is a polynomial of degree 1. The following is a trivial (normally ignored; inconsequential) non-polynomial: (5x2 - 2x2 - 3x2 + 2) ======================================
What is a degree of polynomial?
That means that the monomial of the highest degree has a degree higher than 1. For example: x + 5 3x - 7 -27x + 8
What is a polynomial with a degree of three?
The degree of a polynomial refers to the largest exponent in the function for that polynomial. A degree 3 polynomial will have 3 as the largest exponent, but may also have smaller exponents. Both x^3 and x^3-x²+x-1 are degree three polynomials since the largest exponent is 4. The polynomial x^4+x^3 would not be degree three however because even though there is an exponent of 3, there is a higher exponent also present (in this case, 4).
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 polynomialLinear=Variable raised to the first powerQuadratic=Variable raised to the second power (or "squared")Cubic=Variable raised to the third power (or "cubed")Quartic=Variable raised to the fourth powerQuintic=Variable raised to the fifth powerAnything 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.
How do you find the perimeter of each iteration of a tessellation?
You need to find the perimeter at the first few iterations and find out what the sequence is. It could be an arithmetic sequence or a polynomial of a higher degree: you need to find out the generating polynomial. Then substitute the iteration number in place of the variable in this polynomial.
How do you find the roots of a polynomial of graphed points?
Join the points using a smooth curve. If you have n points choose a polynomial of degree at most (n-1). You will always be able to find polynomials of degree n or higher that will fit but disregard them. The roots are the points at which the graph intersects the x-axis.
Is 18 times y to the cube plus 2 times y to the square plus 1 a polynomial if so what kind?
Yes, 18y3 + 2y2 + 1 is a polynomial; it is a cubic expression. If it were expanded to form an equation, then it would be a cubic equation (or higher), capable of solution.
what is first order?
In mathematics and other formal sciences, first-order or first order most often means either: "linear" (a polynomial of degree at most one), as in first-order approximation and other calculus uses, where it is contrasted with "polynomials of higher degree", or.
Can you get a higher degree than master degree?
A doctor's degree is higher than a master's degree.
What polynomial has more than three terms?
A polynomial of order 3 (a cubic) or higher can have more than three terms. However, the the following polynomial, even though of order 7, has only 2 terms: x7 - 23.
