True or False. In Exercise, use the technique of Exercise 1 to determine graphically whether the given statement is possibly true or definitely false. (We say "possibly true" because two graphs that appear identical on a calculator screen may actually differ by small amounts or at places not shown in the window.)
(1 − x)6 = 1 − 6x + 15x2 − 20x3 + 15x4 − 6x5 + x6
Exercise 1
(a) Confirm the accuracy of the factorization x2 − 5x + 6 = (x − 2)(x − 3) graphically. [Hint: Graph y = x2 − 5x + 6 and y = (x − 2)(x − 3) on the same screen. If the factorization is correct, the graphs will be identical (which means that you will see only a single graph on the screen).]
(b) Show graphically that (x + 5)2 ≠ x2 + 52. [Hint: Graph y = (x + 5)2 and y = x2 + 52 on the same screen. If the graphs are different, then the two expressions cannot be equal.]
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