Questions and Answers
What is the general form of a quadratic expression?
What is the purpose of factorising a quadratic expression?
What is the general form of a factorised quadratic expression?
How do you find the values of p and q when factorising a quadratic expression?
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What is the degree of a cubic expression?
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What is the general form of a cubic expression?
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Study Notes
Algebraic Expressions
Quadratic Expressions
- A quadratic expression is a polynomial expression of degree two, meaning the highest power of the variable (usually x) is two.
- The general form of a quadratic expression is: ax^2 + bx + c, where a, b, and c are constants.
- Examples of quadratic expressions: x^2 + 4x + 4, 2x^2 - 3x - 1, x^2 - 2x - 3
Factorising Quadratics
- Factorising a quadratic expression means expressing it as a product of two binomials.
- The general form of a factorised quadratic expression is: (x + p)(x + q), where p and q are constants.
- To factorise a quadratic expression, find two numbers whose product is the constant term (c) and whose sum is the coefficient of the linear term (b).
- Examples of factorising quadratics:
- x^2 + 5x + 6 = (x + 3)(x + 2)
- x^2 - 4x - 3 = (x - 3)(x + 1)
Cubic Expressions
- A cubic expression is a polynomial expression of degree three, meaning the highest power of the variable (usually x) is three.
- The general form of a cubic expression is: ax^3 + bx^2 + cx + d, where a, b, c, and d are constants.
- Examples of cubic expressions: x^3 + 2x^2 - 7x - 1, 2x^3 - 3x^2 - 5x + 2, x^3 - 2x^2 - 3x + 1
- Factoring cubic expressions can be more complex than quadratic expressions, and may require the use of algebraic methods such as the Rational Root Theorem.
Algebraic Expressions
Quadratic Expressions
- Quadratic expressions are polynomials of degree two, where the highest power of the variable (usually x) is two.
- The general form of a quadratic expression is: ax^2 + bx + c, where a, b, and c are constants.
- Examples of quadratic expressions include: x^2 + 4x + 4, 2x^2 - 3x - 1, and x^2 - 2x - 3.
Factorising Quadratics
- Factorising a quadratic expression involves expressing it as a product of two binomials.
- The general form of a factorised quadratic expression is: (x + p)(x + q), where p and q are constants.
- To factorise a quadratic expression, find two numbers whose product is the constant term (c) and whose sum is the coefficient of the linear term (b).
- Examples of factorising quadratics include:
- x^2 + 5x + 6 = (x + 3)(x + 2)
- x^2 - 4x - 3 = (x - 3)(x + 1)
Cubic Expressions
- Cubic expressions are polynomials of degree three, where the highest power of the variable (usually x) is three.
- The general form of a cubic expression is: ax^3 + bx^2 + cx + d, where a, b, c, and d are constants.
- Examples of cubic expressions include: x^3 + 2x^2 - 7x - 1, 2x^3 - 3x^2 - 5x + 2, and x^3 - 2x^2 - 3x + 1.
- Factoring cubic expressions can be more complex than quadratic expressions and may require the use of algebraic methods such as the Rational Root Theorem.
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Learn about quadratic expressions, their general form, and how to factorize them. Practice with examples and strengthen your algebra skills.