[u]Distributive property:[/u][br][br][math]a\left(b+c\right)=ab+ac[/math][br][br]You multiply what is outside the parenthesis to everything that is inside the parenthesis.[br][br]Example:[br][math]3\left(x+2\right)=3x+6[/math][br][br]Special case: Distributing a negative means negating everything inside the parenthesis.[br][br][math]-\left(x^2+2x-6\right)=-x^2-2x+6[/math]

[u]Degree of a monomial:[br][br][/u]The degree of a monomial the sum of the exponents of its variables.[br]Example: The degree of [math]x^5y^8z^2[/math] is 5+8+2 = 12.

The degree of a polynomial is the degree of the highest degree term. [br][br]The degree of the polynomial [math]7x^3-4x^2+2x+9[/math] is 3, because the highest power of the variable “x” is 3.  [br][br][br]

To add two polynomials, add all of the like terms.[br][br]Example: [math]\left(p^3+2p^2-3p\right)+\left(3p^2+2p-5\right)=p^3+5p^2-p-5[/math][br][br]To subtract two polynomials, first negate the terms in the second polynomial and then add like terms.[br]Example: [math]\left(2x^2+3x-2\right)-\left(x^2-2x-7\right)=\left(2x^2+3x-2\right)+\left(-x^2+2x+7\right)=x^2+5x+5[/math]

To find the GCF of the terms of a polynomial, do prime factorization of each term and find the common factors.[br][br]Example: [math]15x^2+12x[/math][br][br]The first term [math]15x^2[/math] factors as [math]3\cdot5\cdot x\cdot x[/math][br][br]The second term [math]12x[/math] factors as [math]3\cdot4\cdot x[/math][br][br]In both terms you see [math]3\cdot x[/math][br]So the GCF = [math]3x[/math]