12) Wendy is creating a board game. She wants to cut square game pieces that 1
measure 1 inches on each side from a piece of paper that measures 9 inches by 9
2
inches. How many game pieces can Wendy cut from the paper?

36

Step-by-step explanation: I used a calculator to multiply 9 by 9 & 1 1/2 by 1 1/2. For 9 by 9 you get 81, for 1 1/2 by 1 1/2 you get 2 1/4. 81 divided by 2 1/4 is 36. You’re welcome sorry if I’m late!

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.