Chapter 5: Exercises with Solutions

Section 5.3Zeros of the Quadratic100y100y(−4,64)x20x20f(x)=−(x+4) 2 +64f(x)=−(x+4) 2 +6431. Using the ac-test, first look for two numbers whose product is ac = (42)(−2) =−84 and whose sum is b = 5. The solutions are −7 and 12. Then42x 2 + 5x − 2 = 42x 2 − 7x + 12x − 2= 7x(6x − 1) + 2(6x − 1)= (7x + 2)(6x − 1)Now verify the factorization by multiplying (7x + 2)(6x − 1) to obtain 42x 2 + 5x − 2.33. Using the ac-test, first look for two numbers whose product is ac = (5)(12) = 60and whose sum is b = −19. The solutions are −4 and −15. Then5x 2 − 19x + 12 = 5x 2 − 4x − 15x + 12= x(5x − 4) − 3(5x − 4)= (x − 3)(5x − 4)Now verify the factorization by multiplying (x − 3)(5x − 4) to obtain 5x 2 − 19x + 12.35. Using the ac-test, first look for two numbers whose product is ac = (−4)(−5) = 20and whose sum is b = 9. The solutions are 4 and 5. Then− 4x 2 + 9x − 5 = −4x 2 + 4x + 5x − 5= 4x(−x + 1) − 5(−x + 1)= (4x − 5)(−x + 1)Now verify the factorization by multiplying (4x − 5)(−x + 1) to obtain −4x 2 + 9x − 5.Version: Fall 2007