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Are there only 3 degree's in a polynomial equation?
No. A polynomial can have as many degrees as you like.
How many terms does the polynomial have?
As many as you like. A polynomial in 1 variable, and of degree n, can have n+1 terms where n is any positive integer.
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.
How do you find the function for a function table?
It is easy to prove that it is impossible.Given any set of n input and output values, of x and f(x) values, it is easy to prove that there is at least one polynomial of degree n-1 which will fit them. There are, therefore, infinitely many polynomials that will fit these n pairs and any additional pair of the infinitely many choices for the "next" x and f(x).It is easy to prove that it is impossible.Given any set of n input and output values, of x and f(x) values, it is easy to prove that there is at least one polynomial of degree n-1 which will fit them. There are, therefore, infinitely many polynomials that will fit these n pairs and any additional pair of the infinitely many choices for the "next" x and f(x).It is easy to prove that it is impossible.Given any set of n input and output values, of x and f(x) values, it is easy to prove that there is at least one polynomial of degree n-1 which will fit them. There are, therefore, infinitely many polynomials that will fit these n pairs and any additional pair of the infinitely many choices for the "next" x and f(x).It is easy to prove that it is impossible.Given any set of n input and output values, of x and f(x) values, it is easy to prove that there is at least one polynomial of degree n-1 which will fit them. There are, therefore, infinitely many polynomials that will fit these n pairs and any additional pair of the infinitely many choices for the "next" x and f(x).
What do you know about the most possible number of zeros for a polynomial?
A polynomial can have as many 0s as its order - the power of the highest term.A polynomial can have as many 0s as its order - the power of the highest term.A polynomial can have as many 0s as its order - the power of the highest term.A polynomial can have as many 0s as its order - the power of the highest term.
At most how many unique roots will a fourth degree polynomial have?
4, the same as the degree of the polynomial.
Are there only 3 degree's in a polynomial equation?
No. A polynomial can have as many degrees as you like.
How many terms can a polynomial have?
As many as you like. The highest power of the variable in question (usually x) defines the degree of the polynomial. If the degree is n, the polynomial can have n+1 terms. (If there are more then the polynomial can be reduced.) But there is NO LIMIT to the value of n.
How many real roots will a 3rd degree polynomial have?
A third degree polynomial could have one or three real roots.
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.)
At most how many unique roots will a third-degree polynomial have?
A third-degree equation has, at most, three roots. A fourth-degree polynomial has, at most, four roots. APEX 2021
How many terms does the polynomial have?
As many as you like. A polynomial in 1 variable, and of degree n, can have n+1 terms where n is any positive integer.
At most, how many unique roots will a fourth-degree polynomial have?
Four.Four.Four.Four.
How many extreme points does a degree of 4 have?
A polynomial of degree 4 can have up to 3 local maxima/minima.
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.
How many unique roots will a third degree polynomial function have?
It can have 1, 2 or 3 unique roots.
What kind of sequence is the pattern 1 6 7 13 20?
There are many possible answers. But given 5 points, an answer that can be guaranteed is that it is a polynomial of degree 4 (a quartic).In this case, Un = (-13n4 + 166n3 - 719n2 + 1310n - 720)/24There are many possible answers. But given 5 points, an answer that can be guaranteed is that it is a polynomial of degree 4 (a quartic).In this case, Un = (-13n4 + 166n3 - 719n2 + 1310n - 720)/24There are many possible answers. But given 5 points, an answer that can be guaranteed is that it is a polynomial of degree 4 (a quartic).In this case, Un = (-13n4 + 166n3 - 719n2 + 1310n - 720)/24There are many possible answers. But given 5 points, an answer that can be guaranteed is that it is a polynomial of degree 4 (a quartic).In this case, Un = (-13n4 + 166n3 - 719n2 + 1310n - 720)/24
