ACT Math Elementary Algebra Polynomials FOIL Factoring GCF Trinomials Difference of Squares

Elementary Algebra — Polynomials: FOIL, Factoring — GCF, Trinomials, Difference of Squares

What This Is and Why It Matters for the ACT

Elementary Algebra — Polynomials, including FOIL, Factoring, GCF, Trinomials, and Difference of Squares, appears on the ACT Math section. It's a moderately difficult topic that requires a solid understanding of algebraic concepts. You'll encounter these concepts on approximately 20-25% of the Math questions.

Key Concepts (What You Must Know)

• FOIL method: Multiply two binomials by multiplying the First, Outer, Inner, and Last terms.
• Factoring: Break down an expression into simpler components, often using the GCF.
• GCF (Greatest Common Factor): The largest factor that divides all terms in an expression.
• Trinomials: Expressions with three terms, often in the form of ax^2 + bx + c.
• Difference of Squares: A special factoring pattern: a^2 - b^2 = (a + b)(a - b).

Step-by-Step Strategy for This Topic

1. Read carefully: Understand the problem and identify the key elements.
2. Identify the type of problem: Is it FOIL, factoring, GCF, trinomials, or difference of squares?
3. Use the correct method: Apply the relevant formula or technique.
4. Check your work: Verify that your answer makes sense and is consistent with the problem.
5. Manage your time: Allocate 1-2 minutes per question, depending on the complexity.

⚠️ Don't forget to check your units: Make sure your answer has the correct units (e.g., meters, seconds).

How It's Tested on the ACT

• Math: Multiple-choice questions with five answer choices.
• Common distractors: Incorrect answers that are close to the correct answer, but not quite right.
• Spotting distractors: Look for answers that are mathematically plausible, but incorrect.

Common Mistakes & Exam Traps

1. The mistake: Not checking units.
   • Why it happens: Rushing or not paying attention to details.
   • How to avoid it: Double-check your units to ensure accuracy.
   • Exam board insight: Incorrect units can lead to a wrong answer.
2. The mistake: Not using the correct method.
   • Why it happens: Misunderstanding the problem or not reading carefully.
   • How to avoid it: Identify the type of problem and use the correct method.
   • Exam board insight: Using the wrong method can lead to a wrong answer.
3. The mistake: Not factoring correctly.
   • Why it happens: Misunderstanding the GCF or not factoring properly.
   • How to avoid it: Use the GCF to break down the expression and factor correctly.
   • Exam board insight: Incorrect factoring can lead to a wrong answer.
4. The mistake: Not simplifying the expression.
   • Why it happens: Not combining like terms or not simplifying the expression.
   • How to avoid it: Simplify the expression by combining like terms.
   • Exam board insight: A simplified expression is often the correct answer.
5. The mistake: Not checking the answer.
   • Why it happens: Rushing or not verifying the answer.
   • How to avoid it: Check your answer to ensure it makes sense and is consistent with the problem.
   • Exam board insight: A wrong answer can be penalized.

Practice Questions (3-5 questions)

Question 1
What is the product of (x + 3) and (x - 2)?

A) x^2 + x - 6 B) x^2 - x - 6 C) x^2 + 5x - 6 D) x^2 - 5x - 6 E) x^2 + 5x + 6

Answer: B) x^2 - x - 6 Explanation: Use the FOIL method to multiply the binomials.

Question 2
What is the GCF of 12x^2 and 18x^3?

A) 2x B) 3x C) 6x D) 12x E) 18x

Answer: B) 3x Explanation: Identify the GCF by finding the largest factor that divides both terms.

Question 3
What is the factored form of x^2 + 5x + 6?

A) (x + 2)(x + 3) B) (x + 3)(x + 2) C) (x + 1)(x + 6) D) (x + 2)(x + 1) E) (x + 3)(x + 1)

Answer: A) (x + 2)(x + 3) Explanation: Factor the expression by finding the GCF and breaking it down into simpler components.

Quick Reference Card (60-Second Summary)

• FOIL method: (x + a)(x + b) = x^2 + (a + b)x + ab
• GCF: Find the largest factor that divides all terms in an expression.
• Trinomials: Expressions with three terms, often in the form of ax^2 + bx + c.
• Difference of Squares: a^2 - b^2 = (a + b)(a - b)

If You Get Stuck on Test Day

• Eliminate impossible answers: Get rid of answer choices that are clearly incorrect.
• Make an educated guess: Choose an answer that is mathematically plausible.
• Skip and come back: Move on to the next question and come back to it later.

Related ACT Topics

• Quadratic equations: Expressions in the form of ax^2 + bx + c = 0.
• Systems of equations: Two or more equations with two or more variables.
• Functions: Relations between variables, often in the form of f(x) = ...