Precalc0006to0010-page8

# Precalc0006to0010-page8 - term of the trinomial factor If a...

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(Section 0.7: Factoring Polynomials) 0.7.3 PART C: FACTORING FORMULAS Factoring Formulas Factoring a … Formula Perfect Square Trinomial (PST) a 2 + 2 ab + b 2 = a + b () 2 a 2 ± 2 ab + b 2 = a ± b () 2 Sum of Two Squares (A rule will be provided for a 2 + b 2 when we discuss imaginary numbers in Section 2.1. As is, it is prime for now.) Difference of Two Squares a 2 ± b 2 = a + b () a ± b () Sum of Two Cubes a 3 + b 3 = a + b () a 2 ± ab + b 2 () Difference of Two Cubes a 3 ± b 3 = a ± b () a 2 + ab + b 2 () WARNING 3 : Many math students forgot or never learned the last two formulas. WARNING 4 : In the last two formulas, there is no “2” or “ ± 2 ” coefficient on the ab
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Unformatted text preview: term of the trinomial factor. If a and b have no common factors (aside from 1 and ± 1 ), the trinomial factors are typically prime . Sometimes, people confuse these trinomials with Perfect Square Trinomials (PSTs), which we introduced in Section 0.6, Part E. TIP 3 : In the last two formulas, observe that the binomial factor is “ as expected ”: a + b ( ) for a 3 + b 3 , and a ± b ( ) for a 3 ± b 3 . The visible signs on the right-hand sides follow the pattern : “same,” “different,” and “+.”...
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