This study guide covers factoring for the SAT Math section, including quadratic expressions (using methods like grouping and the AC method), special polynomial forms (difference of squares, perfect square trinomials, and sum/difference of cubes), and solving quadratic equations (using the zero product property and applying them to real-world problems). Practice questions and an answer key are provided. The guide emphasizes the AC method, special polynomial forms, and solving quadratic equations as high-value topics for the exam.

#Factoring: Your Key to SAT Math Success 🔑

Hey there, future math master! Let's break down factoring, a super important skill for the SAT Math section. Think of it like this: we're taking complex puzzles and turning them into easy-to-solve pieces. Ready to get started? Let's go!

Jump to Quadratic Expressions | Jump to Special Polynomials | Jump to Solving Equations | Jump to Practice Questions

#Factoring Quadratic Expressions

#Understanding Factoring Basics

Factoring is like reverse multiplication – we're rewriting a polynomial as a product of its factors.
For a quadratic like $ax^2 + bx + c$ , we're looking for two binomials that multiply back to that original expression.
This skill is HUGE for solving quadratic equations and understanding graphs of quadratic functions. 📈

#Common Factoring Methods

Factoring by Grouping: Group terms with common factors and pull out the greatest common factor (GCF) from each group.
AC Method: Multiply the coefficient of $x^2$ (a) by the constant term (c). Find two numbers that add up to the coefficient of x (b) and multiply to ac. This is your secret weapon for harder quadratics! 💡
Completing the Square: Rewrites the quadratic as $(x + p)^2 + q$ . Super useful for finding the vertex of a parabola.

Key Concept

The AC method is a versatile technique that can be applied to many quadratic expressions. It's a must-know for the SAT!

Example: Factor $x^2 + 6x + 8$

AC Method: $ac = 1 \times 8 = 8$ . We need factors of 8 that add to 6 (which are 2 and 4).
Rewrite: $x^2 + 2x + 4x + 8$
Group & Factor:...

#Factoring: Your Key to SAT Math Success 🔑

Jump to Quadratic Expressions | Jump to Special Polynomials | Jump to Solving Equations | Jump to Practice Questions

#Factoring Quadratic Expressions

#Understanding Factoring Basics

Factoring is like reverse multiplication – we're rewriting a polynomial as a product of its factors.
For a quadratic like $ax^2 + bx + c$ , we're looking for two binomials that multiply back to that original expression.
This skill is HUGE for solving quadratic equations and understanding graphs of quadratic functions. 📈

#Common Factoring Methods

Factoring by Grouping: Group terms with common factors and pull out the greatest common factor (GCF) from each group.
AC Method: Multiply the coefficient of $x^2$ (a) by the constant term (c). Find two numbers that add up to the coefficient of x (b) and multiply to ac. This is your secret weapon for harder quadratics! 💡
Completing the Square: Rewrites the quadratic as $(x + p)^2 + q$ . Super useful for finding the vertex of a parabola.

Key Concept

The AC method is a versatile technique that can be applied to many quadratic expressions. It's a must-know for the SAT!

Example: Factor $x^2 + 6x + 8$

AC Method: $ac = 1 \times 8 = 8$ . We need factors of 8 that add to 6 (which are 2 and 4).
Rewrite: $x^2 + 2x + 4x + 8$
Group & Factor:...

What are the factors of the quadratic expression $x^2 + 5x + 6$ ?

Factoring quadratic and polynomial expressions

Brian Hall

#Factoring: Your Key to SAT Math Success 🔑

#Factoring Quadratic Expressions

#Understanding Factoring Basics

#Common Factoring Methods

How are we doing?

Factoring quadratic and polynomial expressions

Brian Hall

#Factoring: Your Key to SAT Math Success 🔑

#Factoring Quadratic Expressions

#Understanding Factoring Basics

#Common Factoring Methods

How are we doing?