Factoring in Grade 8

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:

1. Look for two numbers whose product is the last term (c) and whose sum is the coefficient of the middle term (b).
2. Write the expression as: x^2 + (sum)x + (product)
3. 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.