Top Heavy Rational Expressions (Edexcel International A Level Maths: Pure 3)
Revision Note
Author
PaulExpertise
Maths
Improper Algebraic Fractions
What are top-heavy (improper) rational expressions (or algrbraic fractions)?
- The degree of the numerator is greater than or equal to the degree of the denominator
How do I simplify top-heavy rational expressions?
- Write as a quotient and a remainder
- The algebraic equivalent of changing a top-heavy fraction to a mixed number
Exam Tip
Remember that simple cases are sometimes the hardest to spot!
Worked example
Quadratic Divisor
What are the degrees of the quotient and remainder when a polynomial is divided by a quadratic divisor?
- Suppose a polynomial of degree is divided by a quadratic divisor
- The quotient q will have degree
- The degree of the remainder r will be less than
- It could be degree 1 (linear)
- Or it could be degree 0 (constant)
How do I divide a polynomial by a quadratic divisor?
- You use polynomial division!
- Step 1
Divide the leading term of the polynomial by the squared term of the divisor- This gives the leading term of the quotient
- Step 2
Multiply this term by the divisor - Step 3
Subtract this from the polynomial to get a new polynomial with a lower degree - Continue these steps until you have an expression with a degree lower than 2
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