Podcast
Questions and Answers
What is the primary goal of factoring an algebraic expression?
What is the primary goal of factoring an algebraic expression?
What is the formula for the difference of squares?
What is the formula for the difference of squares?
What is the first step in factoring a quadratic expression?
What is the first step in factoring a quadratic expression?
What is the purpose of checking your answers by multiplying the factors together?
What is the purpose of checking your answers by multiplying the factors together?
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What is the general form of a quadratic expression?
What is the general form of a quadratic expression?
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What should you always look for in an expression before attempting to factor it further?
What should you always look for in an expression before attempting to factor it further?
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Study Notes
Factoring in Grade 8
What is Factoring?
Factoring is the process of expressing an algebraic expression as a product of simpler expressions.
Types of Factoring:
Greatest Common Factor (GCF)
- The GCF is the largest number that divides evenly into each term of the expression.
- To find the GCF, list the factors of each term and choose the largest common factor.
Factoring Out the GCF
- If an expression has a common factor in each term, it can be factored out.
- For example: 2x + 4 = 2(x + 2)
Difference of Squares
- The difference of squares formula is: a^2 - b^2 = (a + b)(a - b)
- For example: x^2 - 4 = (x + 2)(x - 2)
Factoring Quadratic Expressions
- A quadratic expression is a polynomial of degree two.
- The general form of a quadratic expression is: ax^2 + bx + c
- Factoring quadratic expressions involves finding two binomials that multiply to the given expression.
- For example: x^2 + 5x + 6 = (x + 2)(x + 3)
Steps to Factor a Quadratic Expression:
- Look for two numbers whose product is the last term (c) and whose sum is the coefficient of the middle term (b).
- Write the expression as: x^2 + (sum)x + (product)
- Factor by grouping: (x + ?)(x + ?)
Tips and Tricks:
- Always look for the GCF first.
- Factor out the GCF before trying to factor further.
- Check your answers by multiplying the factors together.
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Description
Learn about the different types of factoring, including the greatest common factor, difference of squares, and factoring quadratic expressions. Practice steps to factor quadratic expressions and get tips for factoring.
