Polynomial long division

Front

What is polynomial long division?

Back

Polynomial long division is a method used to divide a polynomial by another polynomial of the same or lower degree, similar to numerical long division.

Front

What is the first step in polynomial long division?

Back

The first step is to divide the leading term of the dividend by the leading term of the divisor.

Front

How do you find the quotient in polynomial long division?

Back

The quotient is found by performing the division of the leading terms and then multiplying the entire divisor by this quotient term.

Front

What do you do after finding the first term of the quotient?

Back

Subtract the result from the original polynomial (dividend) to find the new polynomial to divide.

Front

What is the role of the remainder in polynomial long division?

Back

The remainder is what is left over after the division process is complete; it can be zero or a polynomial of lower degree than the divisor.

Front

How do you express the final answer in polynomial long division?

Back

The final answer is expressed as the quotient plus the remainder divided by the divisor.

Front

What is the relationship between the degrees of the polynomials in long division?

Back

The degree of the remainder must be less than the degree of the divisor.

Front

Can polynomial long division be used for non-monic polynomials?

Back

Yes, polynomial long division can be used for both monic and non-monic polynomials.

Front

What is a monic polynomial?

Back

A monic polynomial is a polynomial whose leading coefficient (the coefficient of the highest degree term) is 1.

Front

Provide an example of a polynomial long division problem.

Back

Divide (2x^3 + 3x^2 - 5) by (x + 1).