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Even polynomial functions have f(x) = f(-x). For example, if f(x) = x^2, then f(-x) = (-x)^2 which is x^2. therefore it is even. Odd polynomial functions occur when f(x)= -f(x). For example, f(x) = x^3 + x f(-x) = (-x)^3 + (-x) f(-x) = -x^3 - x f(-x) = -(x^3 + x) Therefore, f(-x) = -f(x) It is odd
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Is it possible to add 2 polynomials together and your answer is not a polynomial?
No. Even if the answer is zero, zero is still a polynomial.
What is the difference of odd and even functions?
An even function is symmetric about the y-axis. An odd function is anti-symmetric.
Will the sum of two polynomials always be a polynomial?
Yes. Note that specifically, the sum might be a constant (just a number), or even zero, but it is convenient to include those in the definition of "polynomial".
Is it true that the degree of polynomial function determine the number of real roots?
Sort of... but not entirely. Assuming the polynomial's coefficients are real, the polynomial either has as many real roots as its degree, or an even number less. Thus, a polynomial of degree 4 can have 4, 2, or 0 real roots; while a polynomial of degree 5 has either 5, 3, or 1 real roots. So, polynomial of odd degree (with real coefficients) will always have at least one real root. For a polynomial of even degree, this is not guaranteed. (In case you are interested about the reason for the rule stated above: this is related to the fact that any complex roots in such a polynomial occur in conjugate pairs; for example: if 5 + 2i is a root, then 5 - 2i is also a root.)
What is the difference between difference in kind and difference in degree?
a difference in degree is when it is the same structure but different, a difference in kind is when it doesnt even relate, whole new topic. ex: raindrop and flood, a flood is just many raindrops therefore a difference in degree.
What are some similarities and differences between quartic and cubic functions?
The similarities are that they are polynomial functions and therefore continuous and differentiable.A real cubic will has an odd number of roots (and so must have a solution), a quartic has an even number of roots and so may have no solutions.
What is the relationship between the degree of a polynomial and the number of roots it has?
In answering this question it is important that the roots are counted along with their multiplicity. Thus a double root is counted as two roots, and so on. The degree of a polynomial is exactly the same as the number of roots that it has in the complex field. If the polynomial has real coefficients, then a polynomial with an odd degree has an odd number of roots up to the degree, while a polynomial of even degree has an even number of roots up to the degree. The difference between the degree and the number of roots is the number of complex roots which come as complex conjugate pairs.
How do you determine if a polynomial is the difference of two squares?
"Difference" implies subtraction. Example: The difference of 8 and 5 is 3 because 8 - 5 = 3. To determine if a polynomial is the difference you probably have to subtract one polynomial from another and check if your answer matches a given polynomial. To clarify the above, the polynomial should be able to be factorised into two distinct factors. For example x^2 - y^2 = (x + y)(x - y). This is the difference of two squares.
What are the attributes of a polynomial expression that is a difference of squares?
All terms have even powers, factorable to the form (a+b)(a-b)
How alike polynomials and nonpolynomials?
"Non-polynomials" may be just about anything; how alike or different they are will depend on what specific restrictions you put on such functions, or whether you are even talking about functions.
Is it possible to add 2 polynomials together and your answer is not a polynomial?
No. Even if the answer is zero, zero is still a polynomial.
What is the difference of odd and even functions?
An even function is symmetric about the y-axis. An odd function is anti-symmetric.
The difference of two even number is always an even number?
Yes, the difference between two even numbers is always an even number.
What is the difference between the expressions even if and even though?
one is conditional (even IF) and one is not.
What is the difference between the two even numbers?
Subtract the two numbers to get their difference.
What Is the difference between William Shakespeare and Even Shakespeare?
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What do you notice when you find the difference between two odd numbers?
The difference is an even number.
