Precalc0006to0010-page9 - square of a binomial with integer...

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(Section 0.7: Factoring Polynomials) 0.7.4 PART D: TEST FOR FACTORABILITY and PRACTICE EXAMPLES Test for Factorability This test applies to any quadratic trinomial of the form ax 2 + bx + c , where a , b , and c are nonzero, integer coefficients. (Assume the GCF is 1 or ± 1 ; if it is not, factor it out.) The discriminant of the trinomial is b 2 ± 4 ac . • If the discriminant is a perfect square (such as 0, 1, 4, 9, etc.; these are squares of integers), then the trinomial can be factored over the integers . For example, x 2 + 3 x + 2 has discriminant 1 and can be factored as x + 2 () x + 1 () . •• In fact, if the discriminant is 0, then the trinomial is a perfect square trinomial (PST) and can be factored as the
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Unformatted text preview: square of a binomial with integer coefficients. For example, x 2 ± 6 x + 9 has discriminant 0 and can be factored as x ± 3 ( ) 2 . • If the discriminant is not a perfect square, then the trinomial is prime over the integers . This test may be applied in Example Set 5, a) through g), which serve as review exercises for the reader. • The discriminant is denoted by ± (uppercase delta), though that symbol is also used for other purposes. It is seen in the Quadratic Formula in Section 0.11. We will discuss a method for factoring quadratic trinomials using the Quadratic Formula in Chapter 2....
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This document was uploaded on 12/29/2011.

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