p.673 Extra Credit Answer Key for 12.1-12.4

COPY PROBLEMS & SHOW WORK WHENEVER POSSIBLE!
1.  3        2.  4        3.  3
For #4-5, simply combine like terms.
4.  2y² + 6y - 9        5.  -2b² - 7b - 14
6.  First distribute the 3k². Then combine like terms.
   3k²(2 - k) + 18k⁴
= 6k² - 3k³ + 18k⁴   (Now simply reorder the terms so that they are in decreasing degree of k.)
= 18k⁴ - 3k³ + 6k²
For #7-8, when adding polynomials, simply combine like terms.
7.  15x² - 12x        8.  -x³ + 3x² - 2x
9.  When subtracting polynomials, first distribute the minus sign across the terms of the second polynomial, then combine like terms.
   (x³ - x² + 7x) - (2x³ + x + 1)
= x³ - x² + 7x - 2x³ - x - 1
= -x³ - x² + 6x - 1
10. a)  x + 5 + x
         = 2x + 5
      b) x + 3 + x
         = 2x + 3
      c)  To get the area of the rectangle, multiply the width in part a) by the length in part b) by using the FOIL method.
    (2x + 5)(2x + 3)
= 4x² + 6x + 10x + 15
= 4x² + 16x + 15
11.  (3b + 4)(b - 7)  Use the FOIL method.
   = 3b² - 21b + 4b - 28
   = 3b² - 17b - 28
12.  (9p - 1)(9p - 1)
   = 81p² - 9p - 9p + 1
   = 81p² - 18p + 1
13.  (n - 8)(3n - 5)
   = 3n² - 5n - 24n + 40
   = 3n² - 29n + 40