Algebra and Trigonometry (3rd Edition) by Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger

By Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger

Those authors have created a publication to actually aid scholars visualize arithmetic for greater comprehension. through growing algebraic visible side-by-sides to resolve a variety of difficulties within the examples, the authors express scholars the connection of the algebraic resolution with the visible, frequently graphical, resolution. additionally, the authors have additional a number of new instruments to aid scholars higher use the publication for optimum effectiveness not to in simple terms cross the path, yet really comprehend the material.

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Extra resources for Algebra and Trigonometry (3rd Edition) (Beecher/Penna/Bittinger Series)

Example text

X Ϫ y͒2 Ϫ z 2 xϪyϩz 2 2 Ϭ ͑x ϩ y͒ Ϫ z xϩyϪz 5a ab 4b ϩ 2 2ϩ aϪb a Ϫb aϩb 42. 6a 3b 5 6a2 ϩ 9ab ϩ 3b 2 ϩ 5 Ϫ ϩ 2 a Ϫ b b Ϫ a a Ϫ b2 ͑a ϩ b͒ ͑a Ϫ b͒ 22. ͑a ϩ b͒2 Ϫ 9 a Ϫ b Ϫ 3 a ϩ b Ϫ 3 и ͑a Ϫ b͒2 Ϫ 9 a ϩ b ϩ 3 a Ϫ b ϩ 3 43. 7 xϩ8 3x Ϫ 2 Ϫ ϩ Ճ x ϩ 2 4 Ϫ x 2 4 Ϫ 4x ϩ x 2 44. 6 xϩ4 2x Ϫ 3 Ϫ ϩ Ճ x ϩ 3 9 Ϫ x 2 9 Ϫ 6x ϩ x 2 a Ϫ 3b a ϩ 5b ϩ 2 aϩb aϩb 45. 1 x x2 ϩ 2 ϩ ϩ 2 0 xϩ1 2Ϫx x ϪxϪ2 12 5 12y ϩ 5x ϩ x 2y xy 2 x 2y 2 46. xϪ1 xϩ1 xϪ6 Ϫ Ϫ xϪ2 x ϩ 2 4 Ϫ x2 mϩn 36. 1 xϩy cϪ2 xϪyϪz xϩyϩz Add or subtract and, if possible, simplify.

An example is x 2 Ϫ x ϩ 7. There are no real factors of 7 whose sum is Ϫ1. In such a case we say that the polynomial is “not factorable,” or prime. CONNECTING THE CONCEPTS A STRATEGY FOR FACTORING A. Always factor out the largest common factor first. B. Look at the number of terms. Two terms : Try factoring as a difference of squares first. Next, try factoring as a sum or a difference of cubes. Do not try to factor a sum of squares. Three terms : Try factoring as the square of a binomial. Next, try using the FOIL method or the grouping method for factoring a trinomial.

PAIRS OF FACTORS Ϫ1, SUMS OF FACTORS 8 7 1, Ϫ8 Ϫ7 Ϫ2, 4 2 2, Ϫ4 Ϫ2 The numbers we need are 2 and ؊4. We might have observed at the outset that since the sum of the factors is Ϫ2, a negative number, we need consider only pairs of factors for which the negative factor has the greater absolute value. Thus only the pairs 1, Ϫ8 and 2, Ϫ4 need have been considered. Using the pair of factors 2 and Ϫ4, we see that the factorization of x 2 Ϫ 2x Ϫ 8 is ͑x ϩ 2͒ ͑x Ϫ 4͒. Including the common factor, we have x 4 Ϫ 2x 3 Ϫ 8x 2 ෇ x 2͑x ϩ 2͒ ͑x Ϫ 4͒.

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