How to Divide Polynomials by Monomials and Binomials

TL;DR

To divide polynomials by monomials, divide each term in the polynomial separately by the monomial. When dividing by binomials, use long division, which involves arranging terms correctly and finding both the quotient and remainder. Always check your work by multiplying the quotient by the divisor to ensure accuracy.

Transcript

in this lesson we're going to divide a polynomial by a monomial so let's say if we have 12x to the fourth minus 9x cubed plus 15x squared all divided by a single term a monomial in this case 3x squared so what would you do to simplify this expression whenever you're dividing by a single term the best thing to do is to separate the fraction into sma... Read More

Key Insights

• 🗂️ Dividing polynomials by monomials requires dividing each term individually.
• ➗ Long division is used when dividing polynomials by binomials or trinomials.
• ✖️ Checking the answer by multiplying the quotient and divisor helps ensure accuracy.
• ➗ Dividing a binomial by another binomial involves arranging the terms properly and following the long division process.

Questions & Answers

Q: What is the first step when dividing a polynomial by a monomial?

The first step is to separate the fraction into smaller fractions and divide each term in the numerator by the monomial.

Q: How can we divide a trinomial by a binomial?

To divide a trinomial by a binomial, we use long division. Place the numerator (trinomial) inside the long division bracket and the denominator (binomial) outside. Divide, multiply, and subtract according to the long division process.

Q: What should be done when there is a remainder in polynomial division?

If there is a remainder in polynomial division, the answer is the quotient plus the remainder divided by the divisor. This represents the final solution.

Q: How can we check if our quotient is correct in polynomial division?

To check if the quotient is correct in polynomial division, multiply the quotient and the divisor. It should result in the original polynomial numerator.

Summary & Key Takeaways

• Dividing a polynomial by a monomial involves dividing each term in the numerator by the monomial.

• Dividing a polynomial by a binomial requires the use of long division.

• To divide a trinomial by a binomial, use long division and check the answer by multiplying the quotient and divisor.

• In long division, dividing a binomial by another binomial involves arranging the terms properly and finding the quotient and remainder.