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If the polynomial is in terms of the variable x, then look for the term with the biggest power (the suffix after the x) of x. That term is the leading term.
So the leading term of x2 + 5 + 4x + 3x6 + 2x3 is 3x6
If you are likely to do any further work with the polynomial, it would be a good idea to arrange it in order of the descending powers of x anyway.
What else can I help you with?
The rational roots of a polynomial function F(x) can be written in the form where p is a factor of the constant term of the polynomial and q is a factor of the leading coefficient.?
TRue
Can a polynomial term have zero?
Yes.
Degree of a terms of polynomial?
The degree of a polynomial is the highest degree of its terms. The degree of a term is the sum of the exponents of the variables that appear in it.For example, the polynomial 8x2y3 + 5x - 10 has three terms. The first term has a degree of 5, the second term has a degree of 1, and the last term has a degree of 0. Therefore, the polynomial is degree five.
What is the degree of this term 4xy?
It is a polynomial of degree one in x, and also a polynomial of degree one in y.
How do you multiply monomial by a polynomial?
you foil it out.... for example take the first number or variable of the monomial and multiply it by everything in the polynomial...
What is the leading term in a polynomial?
The leading term in a polynomial is the term with the highest degree, which determines the polynomial's end behavior and its classification (e.g., linear, quadratic, cubic). It is typically expressed in the form ( ax^n ), where ( a ) is a non-zero coefficient and ( n ) is a non-negative integer. The leading term is crucial for understanding the polynomial's growth as the input values become very large or very small.
Where p is a factor of the leading coefficient of the polynomial and q is a factor of the constant term.?
Anywhere. Provided it is not zero, and number p can be the leading coefficient of a polynomial. And any number q can be the constant term.
The video example 36 dividing a polynomial by a binomial?
In video example 36, the process of dividing a polynomial by a binomial is demonstrated using long division. The polynomial is divided term by term, starting with the leading term of the polynomial, and determining how many times the leading term of the binomial fits into it. This is followed by multiplying the entire binomial by that quotient term, subtracting the result from the original polynomial, and repeating the process with the remainder until the polynomial is fully divided. The final result includes both the quotient and any remainder expressed as a fraction.
What is type a polynomial with integer coefficients and a leading coefficient of 1 in the box below?
A polynomial with integer coefficients and a leading coefficient of 1 is called a monic polynomial. An example of such a polynomial is ( f(x) = x^3 - 4x^2 + 6x - 2 ). In this polynomial, all coefficients are integers, and the leading term ( x^3 ) has a coefficient of 1.
What is the number in front of the term with the highest degree in a polynomial?
It is the Coefficient. It only refers to the given term that it is front. e.g. 2x^2 - 3x + 1 The '2' in front of 'x^2' only refers to 'x^2'. The '-3' in front of 'x' is the coefficient of '-3' The '1' is a constant.
How DO YOU divide the polynimail by another polynomail?
To divide one polynomial by another, you use polynomial long division or synthetic division. In polynomial long division, you divide the leading term of the dividend by the leading term of the divisor to find the first term of the quotient. Then, multiply the entire divisor by this term and subtract the result from the dividend, repeating the process until the degree of the remainder is less than that of the divisor. The final result consists of the quotient and the remainder expressed as a fraction over the divisor.
Does a polynomial with a leading term with an even exponent must have at least one real zero?
No.
The rational roots of a polynomial function F(x) can be written in the form where p is a factor of the constant term of the polynomial and q is a factor of the leading coefficient.?
TRue
How can you know that a term is polynomial?
A [single] term cannot be polynomial.
How can you find a degree in a polynomial?
The degree of a polynomial is the highest degree of its terms. The degree of a term is the sum of the exponents of the variables that appear in it.7x2y2 + 4x2 + 5y + 13 is a polynomial with four terms. The first term has a degree of 4, the second term has a degree of 2, the third term has a degree of 1 and the fourth term has a degree of 0. The polynomial has a degree of 4.
Can the leading coefficient of a polynomial function be a fraction?
Yes, the leading coefficient of a polynomial function can be a fraction. A polynomial is defined as a sum of terms, each consisting of a coefficient (which can be any real number, including fractions) multiplied by a variable raised to a non-negative integer power. Thus, the leading coefficient, which is the coefficient of the term with the highest degree, can indeed be a fraction.
If you find that a term is missing from a long division polynomial problem you should write that term with a coefficient of?
Zero.
