Polynomial Divided by Monomial Calculator
Here’s a comprehensive guide on dividing polynomials by monomials, presented in a table format:
Dividing Polynomials by Monomials
| Aspect | Details |
|---|---|
| Definition | Dividing a polynomial (multiple terms) by a monomial (single term) |
| Basic Principle | Divide each term of the polynomial by the monomial separately1 |
| Steps | 1. Split the polynomial into individual terms 2. Divide each term by the monomial 3. Combine the results1 |
| Key Rule | Use the quotient rule for exponents: xmxn=xm−nxnxm=xm−n4 |
| Method 1: Splitting Terms | – Set up the division as a fraction – Divide each term in the numerator by the denominator – Simplify each term – Combine the results2 |
| Method 2: Long Division | – Write the polynomial as the dividend – Divide the first term, multiply, subtract, and bring down – Repeat until the remainder’s degree is less than the divisor’s1 |
| Example | (16z3−20z2)÷4z2=16z34z2−20z24z2=4z−5(16z3−20z2)÷4z2=4z216z3−4z220z2=4z−51 |
| Checking the Answer | Multiply the quotient by the divisor; should equal the original polynomial2 |
| Common Mistakes | – Forgetting to divide each term – Incorrect application of exponent rules – Not simplifying completely |
| Special Cases | – When dividing by a constant, only divide the coefficients – Terms may cancel out completely – Result may include fractional terms |
Remember:
- Always ensure the monomial divisor is not zero
- Simplify your answer as much as possible
- Practice with various examples to master the technique
This table provides a concise overview of the key aspects of dividing polynomials by monomials, including methods, rules, and important considerations.