What are algebraic expressions and factors?; How to spot common factors and the GCF.; The steps to factorize algebraic expressions.; Practice examples together.; Why factorization matters in the real world.

Factoring Algebraic Expressions

Mathematics

Factoring Algebraic Expressions

Learn to break down algebraic expressions into simpler parts.

Agenda

• What are algebraic expressions and factors?

• How to spot common factors and the GCF.

• The steps to factorize algebraic expressions.

• Practice examples together.

• Why factorization matters in the real world.

Algebraic Expressions: Intro

Algebraic expressions combine numbers, variables (letters like 'x' or 'y'), and operation signs (+, -, *, /) to show a quantity. For instance, `3x + 7` is an expression that could represent the cost of three tickets plus a $7 booking fee. They are fundamental tools for solving problems and modeling situations in math.

Algebraic expressions use variables like 'x' to represent unknown quantities.

Factors: A Quick Look

• Numbers that multiply to make another number.

• Example: 3 and 4 are factors of 12 (3 x 4 = 12).

• Also, 2 and 6 are factors of 12 (2 x 6 = 12).

• Every number has 1 and itself as factors.

Algebraic Factors Defined

Algebraic factors are expressions that, when multiplied, create another algebraic expression. Similar to how 2 and 3 are factors of 6, for `3x + 6`, the factors are `3` and `(x + 2)` because `3 * (x + 2)` equals `3x + 6`. Identifying these factors is key to understanding and simplifying expressions.

Algebraic expressions: factors help simplify and understand math.

Spotting Common Factors

• **Numbers:** Find the GCF of numerical coefficients (e.g., 12, 18 GCF is 6).

• **Variables:** Identify variables present in *all* terms (e.g., 'x' in 4x + 8xy).

• **Exponents:** Use the lowest power for each common variable (e.g., x² and x³ use x²).

• **Combine:** Multiply all identified common parts (e.g., 6x² from 12x³ + 18x²).

Finding the GCF

The Greatest Common Factor (GCF) is the largest factor, both numerical and variable, that all terms in an expression share. Think of it as the biggest 'chunk' you can pull out of every part. For instance, for the expression `12x^2 + 18x`, the GCF is `6x`.

Factor by grouping: ax + ay + bx + by = (a + b)(x + y).

What is Factorization?

Factorization is the reverse process of multiplication. It's how we break down an algebraic expression into simpler expressions, called its factors. For instance, factoring `3x + 6` results in `3(x + 2)`, where `3` and `(x + 2)` are the factors.

Factoring x² + 5x + 6 into (x + 2)(x + 3).

Why Factorize?

• Simplifies expressions: `x^2 - 4` becomes `(x-2)(x+2)`.

• Solves equations: find `x` in `x^2 - 5x + 6 = 0`.

• Prepares for advanced algebra and higher math.

Step 1: GCF First!

Before doing anything else, always look for the Greatest Common Factor (GCF) in your algebraic expression. This crucial first step simplifies the expression, making the rest of the factorization much easier. For example, in `3x + 6`, the GCF is `3`, so we factor it out first.

Factor polynomials by first finding the Greatest Common Factor.

Factoring Algebraic Expressions

What are algebraic expressions and factors?; How to spot common factors and the GCF.; The steps to factorize algebraic expressions.; Practice examples together.; Why factorization matters in the real world.

People who viewed this slide also liked...