Dividing Polynomials
Divide polynomials by monomials in Grade 9 algebra by splitting each term of the numerator and dividing individually, applying exponent rules to simplify each resulting term.
Key Concepts
New Concept To divide a polynomial by a monomial, divide each term in the numerator by the denominator. What’s next Next, you’ll apply this concept by dividing polynomials by monomials and then use factoring and long division for more complex problems.
Common Questions
How do you divide a polynomial by a monomial?
Split the division across each term in the numerator: (a + b)/c = a/c + b/c. Divide each term separately by the monomial, applying coefficient division and exponent subtraction rules to each term.
How do you simplify (6x⁴ + 9x³ - 3x²) ÷ 3x²?
Divide each term by 3x²: 6x⁴/3x² = 2x², 9x³/3x² = 3x, -3x²/3x² = -1. Combine results: 2x² + 3x - 1. Divide coefficients numerically and subtract exponents for each variable.
What exponent rule applies when dividing powers with the same base?
When dividing xᵐ by xⁿ, subtract the exponents: xᵐ/xⁿ = xᵐ⁻ⁿ. For x⁵/x² = x³. If the exponents are equal, the result is x⁰ = 1. This quotient rule is the inverse of the product rule.