Question

mpm2p - culminating task
task 3: climbing the tower!
now in pisa, your next challenge is to climb to the top of the leaning tower of pisa. as you climb, you must answer a question on every second floor in the tower (there are nine floors in total) to which there may be multiple answers given in the space provided, show your calculations to determine which of the solutions is correct. once you have the correct solution, move on to the next floor of the tower. don’t forget to enjoy the view.

floor	question	show your work	possible answers
4	expand and simplify (2 marks) ((3x + 4)(3x - 4))		(square 6x^2 + 8x - 16) <br> (square 6x^2 + 24x - 16) <br> (square 9x^2 - 16) <br> (square 9x^2 - 8)
6	factor fully (2 marks) (x^2 - 9x + 18)		(square (x + 6)(x + 3)) <br> (square (x - 6)(x - 3)) <br> (square (x - 2)(x - 9)) <br> (square (x + 2)(x + 9))
8	factor fully (3 marks) ((2x^2 - 32))		no possible solution given. you must calculate this one on your own.

congratulations!!! you have successfully climbed the leaning tower of p and can now proceed to rome.

Explanation:

Step1: Expand using FOIL method

$(x+4)(x-6) = x^2 -6x +4x -24$

Step2: Combine like terms

$x^2 + (-6x+4x) -24 = x^2 -2x -24$

Step3: Expand using difference of squares

$(3x+4)(3x-4) = (3x)^2 - 4^2$

Step4: Simplify the expression

$9x^2 - 16$

Step5: Find factors of 18 that sum to -9

Factors of 18: $-6$ and $-3$ (since $-6 + (-3) = -9$, $-6 \times -3 = 18$)

Step6: Write factored form

$x^2 -9x +18 = (x-6)(x-3)$

Step7: Factor out greatest common factor

$2x^2 -32 = 2(x^2 -16)$

Step8: Factor difference of squares

$2(x^2 -4^2) = 2(x+4)(x-4)$

Answer:

Floor 2: $\boldsymbol{x^2 - 2x - 24}$
Floor 4: $\boldsymbol{9x^2 - 16}$
Floor 6: $\boldsymbol{(x-6)(x-3)}$
Floor 8: $\boldsymbol{2(x+4)(x-4)}$