In this Grade 9 Saxon Algebra 1 lesson, students learn to divide polynomials by monomials, binomials, and using polynomial long division, including cases with remainders and zero coefficients. The lesson covers writing division problems as rational expressions, factoring to cancel common factors, and expressing non-zero remainders as rational expressions over the divisor. It is part of Chapter 10: Systems and Problem Solving.
Section 1
📘 Dividing Polynomials
To divide a polynomial by a monomial, divide each term in the numerator by the denominator.
Next, you’ll apply this concept by dividing polynomials by monomials and then use factoring and long division for more complex problems.
Section 2
Dividing a polynomial by a monomial
To divide a polynomial by a monomial, divide each term in the numerator by the denominator.
Think of the polynomial as a party-size sub sandwich and the monomial as your friends. To share it fairly, you cut each section (term) of the sandwich and give a piece to every friend. This way, every part of the polynomial gets divided equally!
Section 3
Dividing a polynomial by a binomial
If possible, factor the numerator and denominator, then divide out any common factors to simplify the expression.
This is the ultimate shortcut for division! It’s like finding matching socks in a messy drawer. Once you spot a matching factor on the top and bottom, you can cancel them out. What’s left over is your much tidier, simplified answer. Easy peasy!
Section 4
Dividing a polynomial using long division
Write the divisor and dividend in descending order before dividing. Use the same steps as numerical long division: divide, multiply, subtract, and bring down.
When factoring fails, long division is your trusty backup plan. Just like with regular numbers, you tackle the polynomial piece by piece. Line everything up neatly, and you'll solve even the trickiest division problems without breaking a sweat. It's old school but it always works!
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Section 1
📘 Dividing Polynomials
To divide a polynomial by a monomial, divide each term in the numerator by the denominator.
Next, you’ll apply this concept by dividing polynomials by monomials and then use factoring and long division for more complex problems.
Section 2
Dividing a polynomial by a monomial
To divide a polynomial by a monomial, divide each term in the numerator by the denominator.
Think of the polynomial as a party-size sub sandwich and the monomial as your friends. To share it fairly, you cut each section (term) of the sandwich and give a piece to every friend. This way, every part of the polynomial gets divided equally!
Section 3
Dividing a polynomial by a binomial
If possible, factor the numerator and denominator, then divide out any common factors to simplify the expression.
This is the ultimate shortcut for division! It’s like finding matching socks in a messy drawer. Once you spot a matching factor on the top and bottom, you can cancel them out. What’s left over is your much tidier, simplified answer. Easy peasy!
Section 4
Dividing a polynomial using long division
Write the divisor and dividend in descending order before dividing. Use the same steps as numerical long division: divide, multiply, subtract, and bring down.
When factoring fails, long division is your trusty backup plan. Just like with regular numbers, you tackle the polynomial piece by piece. Line everything up neatly, and you'll solve even the trickiest division problems without breaking a sweat. It's old school but it always works!
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter