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- Greatest Common Factor: The Greatest Common Factor (GCF) is the largest number which can divide a set of numbers simultaneously.
- You know you have reached the GCF when there is no other number that can divide the set of numbers you are working with simultaneously.
- Polynomials: A polynomial refers to an expression with two or more terms.

Examples of polynomials and their GCF:

- 4x
^{4}+ 2x^{2}+ x = x(4x^{3 }+ 2x + 1) - y
^{5}+ 6y^{3 }+ y^{2 }= y^{2}(y^{3}+ 6y + 1) - z
^{4}+ 2z^{3 }+ z^{2 }+ 7z = z(z^{3 }+ 2z^{2}+ z + 7)

- Rational Expression: Rational expression refers to the quotient of two polynomials.
- Explanation of rational expression: Rational expressions in polynomials are similar to rational numbers in integers.

Examples of rational expressions and their simplified forms:

- 4x + 8/ 4x – 8 = 4(x + 2)/ 4(x – 2) = x + 2/x – 2
- 6z
^{2 }+ 3z/ 3z^{2 }+ 3z = 3z(2z + 1)/3z(z + 3) = 2z + 1/ z + 3

- Factoring the difference of two squares: The model used to factor the difference of two squares is as follows:

a^{2 }– b^{2 }= (a + b) (a – b)

- Factoring perfect square trinomials: The models used to factor perfect square polynomials is as follows:

a^{2} + 2ab + b^{2} = (a + b)^{ 2 }and a^{2} - 2ab + b^{2} = (a - b)^{ 2 }

- All of the above models make sense to me.
- Factoring the difference of two squares seems much easier than factoring perfect square trinomials because in factoring perfect square trinomials, you must first determine whether the expression is a perfect square trinomial. In contrast, the difference of two squares is obvious.

Examples:

- The difference of two squares:

25x^{2 }– 16y^{2 }= (5x – 4y) (5x – 4y)

- Perfect square trinomial;

x^{2 }+ 24x + 144 = (x + 12)^{2}