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The square of the sum of two terms
(a+b)^{2}=a^{2}+2ab+b^{2}
The square of the difference of two terms
(a-b)^{2}=a^{2}-2ab+b^{2}
The product of the sum and the difference of two terms.
(a+b)(a-b)=a^{2}-b^{2}
The product of two binomials having a common term.
(x+a)(x+b)=x^{2}+(a+b)x+ab
Legendre's Identity
(x+y)^{2}+(x-y)^{2}=2(x^{2}+y^{2})
Two methods of synthetic division
Horner's Method
Ruffini's Method
Algebraic Term
formed by a numerical part and a literal part
coefficient
numerical part of an algebraic term
variables with corresponding indices
the literal part of an algebraic term
Algebraic expression
contains one or more algebraic terms
monomial
algebraic expression with one term
polynomial
algebraic expression with more than one term
binomial
has two algebraic terms
trinomial
algebraic expression with three terms
relative degree
degree with respect to a certain variable. it is equal to the index of that variable
absolute degree
it is the sum of the indices of all the variables in a term
Relative degree of a polynomial
it is the degree with respect to a certain variable. It is equal to the highest relative degree with respect to that variable of the terms in the polynomial.
absolute degree of a polynomial
it is the highest absolute degree of the terms in the polynomial.
complete polynomial
contains al the powers of that variable from zero to n