Mathematics 17 - College Algebra and Trigonometry First Semester, A.Y. 2014-2015

Exercise Set I Granario

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I. Write TRUE if the statement is always true. Otherwise, write FALSE.

1. (0,) N = [1,) N.2. The set of even integers is closed under addition (an integer is even if it is divisble by 2).

3. For every a R, we have a0 = 1.4. If x2 Q, then x Q.5. If a, b Qc, then a+ b Qc.6. If a (0, 1), then a2 < 1.7. (0, 1) {0, 1} is a closed interval.8. Let a R. Then there is a real number b such that ab = 1.9. The additive inverse and the multiplicative inverse of any given real number are never

equal to each other.

10. Let A,B,C be sets. If A B 6= , B C 6= and A C 6= then A B C 6= .

II. Factor completely.

1. 12x2 7x 122. 12x2 + 25 + 12

3. 2x2 10x+ 124. 3x2 11xy 4y25. x6 646. x4 + 3x2 + 4

7. x4 + 4

8. x3 3x+ x2 39. x3 7x 6

10. x3 7x+ 611. x3 9x+ 812. x2 2x+ 2xy 2y + y2 + 113. x3 x2 + xy y2 + y3

14. xyz + xy + xz + yz + x+ y

15. 3x2y + 2xy2 3x2z 2xyz 2yz 3xz +2y2 + 3xy

16. (x 1)(x 2)(x 3)(x 4) 24

I know some things, he said. I can, you know, do math and stuff.

- Harry Potter in Harry Potter and the Sorcerers Stone by J.K. Rowling