Master Multi-Step Factoring Polynomials in Algebra 1 with Examples

📚 Quick Study Guide

• 🔢 Greatest Common Factor (GCF): Always factor out the GCF first. This simplifies the polynomial.
• ➗ Factoring by Grouping: Use this method for polynomials with four terms. Group terms and factor out common factors from each group.
• ✨ Difference of Squares: Recognize and factor expressions in the form $a^2 - b^2 = (a + b)(a - b)$.
• ➕ Perfect Square Trinomials: Identify and factor expressions in the form $a^2 + 2ab + b^2 = (a + b)^2$ or $a^2 - 2ab + b^2 = (a - b)^2$.
• 🧮 Trial and Error: For trinomials of the form $ax^2 + bx + c$, use trial and error to find the correct factors.
• 💡 Check Your Work: Always multiply the factors back together to verify your answer.

Practice Quiz

1. Question 1: Factor completely: $2x^3 + 8x^2 + 8x$
1. $2x(x+2)^2$
2. $2x(x^2+4x+4)$
3. $2x(x+2)(x-2)$
4. $2(x^3+4x^2+4x)$
2. Question 2: Factor completely: $3x^2 - 12$
1. $3(x-2)^2$
2. $3(x+2)(x-2)$
3. $(3x+6)(x-2)$
4. $(x+2)(x-2)$
3. Question 3: Factor completely: $x^3 + 5x^2 - 4x - 20$
1. $(x+5)(x-2)^2$
2. $(x+5)(x+2)(x-2)$
3. $(x-5)(x+2)(x-2)$
4. $(x^2-4)(x+5)$
4. Question 4: Factor completely: $4x^2 + 20x + 25$
1. $(2x+5)(2x-5)$
2. $(2x+5)^2$
3. $(4x+5)(x+5)$
4. $(2x-5)^2$
5. Question 5: Factor completely: $5x^3 - 20x$
1. $5x(x-4)(x+4)$
2. $5x(x^2-4)$
3. $5x(x+2)(x-2)$
4. $(5x^2+10x)(x-2)$
6. Question 6: Factor completely: $x^4 - 16$
1. $(x^2+4)(x^2-4)$
2. $(x^2+4)(x+2)(x-2)$
3. $(x+2)^2(x-2)^2$
4. $(x^2-4)^2$
7. Question 7: Factor completely: $2x^2 + 10x + 12$
1. $2(x+3)(x+2)$
2. $(2x+6)(x+2)$
3. $2(x^2+5x+6)$
4. $(x+3)(x+4)$