Solved examples: Factoring simple algebraic expressions using GCF.

📚 Quick Study Guide

• 🔍 Greatest Common Factor (GCF): The largest factor that divides two or more numbers (or terms in an expression) without leaving a remainder.
• 🔢 Factoring: Breaking down an expression into its constituent factors. For example, factoring $6$ gives $2 \times 3$.
• 💡 Steps for Factoring using GCF:
  1. Find the GCF of all terms in the expression.
  2. Divide each term by the GCF.
  3. Write the original expression as the product of the GCF and the resulting expression from the division.
• 📝 Example: Factor $4x + 8$. The GCF of $4x$ and $8$ is $4$. Dividing each term by $4$ gives $x + 2$. Therefore, $4x + 8 = 4(x + 2)$.
• ➗ Key Formula: $ab + ac = a(b + c)$, where $a$ is the GCF.

Practice Quiz

1. Question 1: What is the greatest common factor (GCF) of $6x$ and $9$?
   1. A) 3
   2. B) $x$
   3. C) 6
   4. D) 9
2. Question 2: Factor the expression: $5y - 10$
   1. A) $5(y - 2)$
   2. B) $5(y + 2)$
   3. C) $5y(1 - 2)$
   4. D) $10(y - 1)$
3. Question 3: Factor the expression: $3a + 6b$
   1. A) $3(a + 2b)$
   2. B) $3(a + 6b)$
   3. C) $6(a + b)$
   4. D) $3a(1 + 2b)$
4. Question 4: Factor the expression: $2x^2 + 4x$
   1. A) $2x(x + 2)$
   2. B) $2(x^2 + 2x)$
   3. C) $x(2x + 4)$
   4. D) $4x(x + 1)$
5. Question 5: Factor the expression: $7p - 14q$
   1. A) $7(p - 2q)$
   2. B) $7(p + 2q)$
   3. C) $14(p - q)$
   4. D) $7p(1 - 2q)$
6. Question 6: Factor the expression: $12m + 18n$
   1. A) $6(2m + 3n)$
   2. B) $12(m + n)$
   3. C) $3(4m + 6n)$
   4. D) $6m(2 + 3n)$
7. Question 7: Factor the expression: $9ab - 27ac$
   1. A) $9a(b - 3c)$
   2. B) $9(ab - 3ac)$
   3. C) $9a(b - 27c)$
   4. D) $9b(a - 3c)$