What is the greatest common factor (GCF) of polynomials?

📚 Quick Study Guide

• 🔍 The Greatest Common Factor (GCF) of polynomials is the largest polynomial that divides evenly into all the terms of the given polynomials.
• 🔢 To find the GCF, first find the GCF of the coefficients (numerical part).
• 🌱 Next, identify the lowest power of each common variable present in all terms.
• 💡 The GCF is the product of the GCF of the coefficients and the lowest powers of the common variables.
• 📝 For example, the GCF of $6x^2y$ and $9xy^3$ is $3xy$.
• ➕ When factoring out the GCF, divide each term by the GCF and write the result in parentheses.
• 🧪 Factoring out the GCF is the reverse of the distributive property.

Practice Quiz

1. What is the GCF of $12x^3$ and $18x^2$?
   1. $6x$
   2. $6x^2$
   3. $36x^3$
   4. $36x^5$
2. What is the GCF of $4a^2b$ and $6ab^2$?
   1. $2ab$
   2. $2a^2b^2$
   3. $2a$
   4. $2b$
3. What is the GCF of $15p^4q^2$ and $25p^2q^3$?
   1. $5p^2q^2$
   2. $5p^4q^3$
   3. $5pq$
   4. $25p^2q^2$
4. What is the GCF of $8x^5y^3$ and $16x^2y^4$?
   1. $8x^2y^3$
   2. $8x^5y^4$
   3. $4x^2y^3$
   4. $16x^2y^3$
5. Factor out the GCF from $3x^2 + 6x$.
   1. $3x(x + 2)$
   2. $3(x^2 + 2x)$
   3. $x(3x + 6)$
   4. $3x^2(1 + 2x)$
6. Factor out the GCF from $10a^3b - 15ab^2$.
   1. $5ab(2a^2 - 3b)$
   2. $5(2a^3b - 3ab^2)$
   3. $5ab(2a^2 - 3b^2)$
   4. $5a(2a^2b - 3b^2)$
7. What is the GCF of $24x^3y^2z$ and $36x^2yz^3$?
   1. $12x^2yz$
   2. $12x^3y^2z^3$
   3. $6x^2yz$
   4. $24x^2yz$