Improper Algebraic Fractions (AQA A-Level Mathematics): Quizzes

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Improper Algebraic Fractions
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What makes an algebraic fraction improper?

Numerator degree ≥ denominator degree

What is the degree of a polynomial?

The highest power of the variable

Which method simplifies improper algebraic fractions?

Polynomial long division

How is a simplified improper fraction expressed?

Quotient + (Remainder/Denominator)

Is x2+3xx+2\frac{x^2 + 3x}{x + 2} an improper fraction?

Yes, numerator degree ≥ denominator

What does the remainder over denominator represent?

A proper fraction

What is the first step in polynomial division?

Divide leading term of numerator by denominator

What is x3+2x2+3x+4x+1\frac{x^3 + 2x^2 + 3x + 4}{x + 1} simplified?

x2+x+2+2x+1x^2 + x + 2 + \frac{2}{x + 1}

What is x2+3x+5x+1\frac{x^2 + 3x + 5}{x + 1} simplified?

x+2+3x+1x + 2 + \frac{3}{x + 1}

In the simplified form, what is the quotient?

A polynomial

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