Question

polynomial operations maze
rections: start in the box labeled \start here.\ solve the problem in the box, color the correct
tution and then solve the box adjacent to the solution. continue until you reach \finished.\
start here!
$(3x^4 - 8x) + (2x - 4x^4)$ $-x^4 - 6x$ $(2x - 1)(7x - 2)$ $14x^2 - 11x + 2$ $x^3 - (x^3 + 9x - 3)$
$x^4 + 6x$ $5x^4 - 12x$ $9x^2 - 3$ $2x^2 - 9x - 3$ $-9x + 3$
$dfrac{3x}{3x^2}$ $x^4 - 6x^3 - 3x$ $(6x - 5x^4) - (4x^4 + 6x^3 + 3x)$ $12x^2 - 6x$ $3x(4x - 2)$
$1$ $-9x^4 - 6x^3 + 3x$ $-x^4 + 9x$ $-2x^4 + x^3 - 3x$ $7x^2 - 5x$
$(3x - 7)^2$ $9x^2 - 42x + 49$ $dfrac{7x^3}{14x}$ $2x^{-1}$ $(5x^3 - 5x - 1) + (5x + 6)$
$9x^2 - 49$ $3x^2 - 14$ $dfrac{1}{2}x^2$ $8x^3 + 55x^2 - 8x - 7$ $5x^3 + 5$
$(5x^2 + 1) + (2 - x)$ $7x^2 - x + 3$ $(x + 7)(8x^2 - x - 1)$ $8x^2 + 6$ $2x(5x^2 + x)$
$5x^2 + 2$ $x^2 - 8x + 12$ $-7x^2 + x$ $9x^2 + 7x - 7$ $10x^3 + 2x^2$
$(x - 4)(x + 4)$ $x^2 + 16$ finished! $4x^2 + 3x + 7$ $(7x^2 - x + 4) - (3x^2 - 4x - 3)$

Explanation:

Step1: Solve the starting box

Combine like terms:
$$(3x^4 - 8x) + (2x - 4x^4) = (3x^4 - 4x^4) + (-8x + 2x) = -x^4 - 6x$$

Step2: Move to adjacent box

Solve $(2x - 1)(7x - 2)$ using FOIL:
$$(2x)(7x) + (2x)(-2) + (-1)(7x) + (-1)(-2) = 14x^2 - 4x -7x +2 = 14x^2 -11x +2$$

Step3: Move to adjacent box

Solve $x^2 - (x^2 +9x -3)$ by distributing the negative:
$$x^2 -x^2 -9x +3 = -9x +3$$

Step4: Move to adjacent box

Solve $3x(4x -2)$ using distribution:
$$3x(4x) + 3x(-2) = 12x^2 -6x$$

Step5: Move to adjacent box

Solve $(6x -5x^4) - (4x^4 +6x^3 +3x)$ by distributing the negative:
$$6x -5x^4 -4x^4 -6x^3 -3x = (-5x^4-4x^4) -6x^3 +(6x-3x) = -9x^4 -6x^3 +3x$$

Step6: Move to adjacent box

Solve $(3x-7)(3x-7)=(3x-7)^2$ using square of binomial:
$$(3x)^2 -2(3x)(7) +7^2 =9x^2 -42x +49$$

Step7: Move to adjacent box

Solve $(5x^2 +1)+(2-x)$ by combining like terms:
$$5x^2 -x +(1+2)=5x^2 -x +3$$

Step8: Move to adjacent box

Solve $(x+7)(8x^2 -x -1)$ using distribution:
$$x(8x^2 -x -1)+7(8x^2 -x -1)=8x^3 -x^2 -x +56x^2 -7x -7=8x^3 +55x^2 -8x -7$$

Step9: Move to adjacent box

Solve $2x(5x^2 +x)$ using distribution:
$$2x(5x^2)+2x(x)=10x^3 +2x^2$$

Step10: Move to adjacent box

Solve $(7x^2 -x +4)-(3x^2 -4x -3)$ by distributing the negative:
$$7x^2 -x +4 -3x^2 +4x +3=(7x^2-3x^2)+(-x+4x)+(4+3)=4x^2 +3x +7$$

Step11: Move to adjacent box

Reach the "Finished!" box.

Answer:

The path through the maze is:

1. $(3x^4 - 8x) + (2x - 4x^4)$ → $-x^4 -6x$
2. $(2x - 1)(7x - 2)$ → $14x^2 -11x +2$
3. $x^2 - (x^2 +9x -3)$ → $-9x +3$
4. $3x(4x -2)$ → $12x^2 -6x$
5. $(6x -5x^4) - (4x^4 +6x^3 +3x)$ → $-9x^4 -6x^3 +3x$
6. $(3x-7)(3x-7)=(3x-7)^2$ → $9x^2 -42x +49$
7. $(5x^2 +1)+(2-x)$ → $5x^2 -x +3$
8. $(x+7)(8x^2 -x -1)$ → $8x^3 +55x^2 -8x -7$
9. $2x(5x^2 +x)$ → $10x^3 +2x^2$
10. $(7x^2 -x +4)-(3x^2 -4x -3)$ → $4x^2 +3x +7$
11. Finished!