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How can you tell if a binomial divides evenly into a polynomial?

Do the division, and see if there is a remainder.


When dividing a polynomial F x by the binomial x - a a remainder not equal to zero tells you that x - a is not a of the polynomial?

factor


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.


How do you find the quotient of a binomial or polynomial when it has a remainder?

To find the quotient of a binomial or polynomial when there is a remainder, perform polynomial long division or synthetic division. Divide the leading term of the dividend by the leading term of the divisor to get the first term of the quotient. Multiply the entire divisor by this term and subtract the result from the dividend, bringing down the next term as needed. Continue this process until you reach a remainder that is of lower degree than the divisor, which can be expressed as ( \text{Quotient} + \frac{\text{Remainder}}{\text{Divisor}} ).


Which binomial is a factor of the polynomial below?

To determine which binomial is a factor of a given polynomial, you can apply the Factor Theorem. According to this theorem, if you substitute a value ( c ) into the polynomial and it equals zero, then ( (x - c) ) is a factor. Alternatively, you can perform polynomial long division or synthetic division with the given binomials to see if any of them divides the polynomial without a remainder. If you provide the specific polynomial and the binomials you're considering, I can assist further.

Related Questions

How can you tell if a binomial divides evenly into a polynomial?

Do the division, and see if there is a remainder.


When dividing a polynomial F x by the binomial x - a a remainder not equal to zero tells you that x - a is not a of the polynomial?

factor


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.


How do you find the quotient of a binomial or polynomial when it has a remainder?

To find the quotient of a binomial or polynomial when there is a remainder, perform polynomial long division or synthetic division. Divide the leading term of the dividend by the leading term of the divisor to get the first term of the quotient. Multiply the entire divisor by this term and subtract the result from the dividend, bringing down the next term as needed. Continue this process until you reach a remainder that is of lower degree than the divisor, which can be expressed as ( \text{Quotient} + \frac{\text{Remainder}}{\text{Divisor}} ).


Which binomial is a factor of the polynomial below?

To determine which binomial is a factor of a given polynomial, you can apply the Factor Theorem. According to this theorem, if you substitute a value ( c ) into the polynomial and it equals zero, then ( (x - c) ) is a factor. Alternatively, you can perform polynomial long division or synthetic division with the given binomials to see if any of them divides the polynomial without a remainder. If you provide the specific polynomial and the binomials you're considering, I can assist further.


Is a binomial a polynomial?

yes a binomial is a polynomial


Is a binomial also a polynomial?

yes a binomial is a polynomial


Is a polynomial also a binomial?

yes a binomial is a polynomial


What is the relationship between binomial and a polynomial?

A binomial is a polynomial with exactly 2 terms.


This is a polynomial with two terms?

binomial


What is 2n 4 plus 3n a monomial a binomial or a polynomial?

It is a binomial, which is also a polynomial.


What is the binomial?

A binomial is a polynomial with two terms.