Factoring by Grouping
Objective: Solve equations by factoring.
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Quadratic equations are equations such as
A quadratic equation is an equation equivalent to one of the form
where a, b, and c are real numbers and
Quadratics are second­degree equations because the largest exponent is a 2.
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Solve
or
The solution set is
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Polynomial equations are equations such as
x3 + 2x2 ­ x + 5 = 0 , x5 + 6x2 ­ 9 = 0 , x2 ­ x = 0
A polynomial equation is an equation that is constructed from one or more variables and constants, using only the operations of addition, subtraction, multiplication, and constant positive whole number exponents.
The degree of a polynomial is determined by the largest exponent.
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Factoring when you have four terms
Solve
What do the first two terms have in common?
Factor out (x­1) from both terms.
Factor the quadratic.
The solution set is
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Solve
x3 + 3x2 ­ x ­ 3 = 0
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Hmwk: page 998 (88 ­ 92)
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