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Unit Five

Key Concepts

- you can

find the product of two binomials by multiplying each term In one binomial by

each term in the other binomial (FOIL). If necessary, simplify by collecting

like terms.

-when

squaring a binomial, you add the two equal middle terms after expansion e.g.

(a+b)²= a²+2ab+b²

- when you

multiply the sum and difference of two terms, the two middle terms are opposites,

so they add to zero e.g. (a+b)(a-b)= a²-b²

- factoring a polynomial is opposite to expanding a polynomial

- to find the GCF of a polynomial, find the GCF of the

coefficients, and then find the GCF of the variable parts

- to factor a polynomial, remove the GCF as the first factor

and then divide each term by the GCF to obtain the second factor.

- For polynomials with more than one variable, the GCF of the

variable parts is the product of the common bases with the least exponent

- a common factor is not necessarily a monomial

- to factor by grouping, factor groups of two terms with a

common factor to produce a binomial common factor

- to factor a quadratic expression of the form x² + bx + c,

first find two integers whose product is c and whose sum is b

- not all quadratic expressions of the form x² + bx + c can

be factored over the integers

-always look for a common factor first, when factoring a

trinomial

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