diff --git a/Grade 10/Math/MPM2DZ/Factoring Quiz.md b/Grade 10/Math/MPM2DZ/Factoring Quiz.md index 046560a..302b481 100644 --- a/Grade 10/Math/MPM2DZ/Factoring Quiz.md +++ b/Grade 10/Math/MPM2DZ/Factoring Quiz.md @@ -1,6 +1,57 @@ -## Level 1 +# Level 1 -a. $`2x^`4 - 32$ - - $`= 2(x^4-16)`$ - - $`= 2((x^2-4)(x^2+4)`$ - - $`= 2((x+2)(x-2)(x^2+4))`$ \ No newline at end of file +## $`2x^4 - 32`$ +- $`= 2(x^4-16)`$ +- $`= 2((x^2-4)(x^2+4)`$ +- $`= 2((x+2)(x-2)(x^2+4)) \\`$ + +## $`2x^2+11x-21`$ +- $`=2x^2+11x-21`$ +- $`\quad \quad 2 \quad -3`$ +- $`\quad \quad 1 \quad \quad 7`$ +- $` = (2x+3)(x+7)`$ + +## $`x^3y^2 + 2x^2y^2-3xy^2`$ +- $`=xy^2(x^2+2x-3)`$ +- $`\quad \quad \quad \quad 1 \quad -1`$ +- $`\quad \quad \quad \quad 1 \quad \quad 3`$ +- $`= xy^2(x-1)(x+3)`$ + +# Level 2 + +## $`4x^4-9x^2+30x-25`$ +- $`=4x^4-(9x^2-30x+25)`$ +- $`\quad \quad \quad \quad \quad \quad 3 \quad -5`$ +- $`\quad \quad \quad \quad \quad \quad 3 \quad -5`$ +- $`= 4x^4 - (3x-5)^2`$ +- $`= (2x^2-3x+5)(2x^2+3x-5)`$ +- $`\quad \quad \quad \quad \quad \quad \quad \quad \quad 2 \quad \quad 5`$ +- $`\quad \quad \quad \quad \quad \quad \quad \quad \quad 1 \quad -1`$ +- $` = (2x^2-3x+5)(2x+5)(x-1)`$ + +## $`3(x-y)^2 - 5x + 5y - 2`$ +- $`= 3(x-y)^2 -5(x-y) - 2`$ +- $`\text{Let } a = (x-y)`$ +- $`= 3a^2 - 5a - 2`$ +- $` \quad \quad 3 \quad \quad 1`$ +- $` \quad \quad 1 \quad -2 `$ +- $`= (3a+1)(a-2)`$ +- $`=(3(x-y)+1)(x-y-2)`$ +- $`=(3x-3y+1)(x-y-2)`$ + +# Level 3 + +## $`x^8 - 17x^4 - 48`$ +- $`\text{Let } y = x^4`$ +- $`= y^2 - 13y - 48`$ +- $`\quad \quad 1 \quad \quad 3`$ +- $`\quad \quad 1 \quad -16`$ +- $`=(y+3)(y-16)`$ +- $`=(x^4+3)(x^4-16)`$ +- $`=(x^4+3)(x^2-4)(x^2+4)`$ +- $`=(x^4+3)(x-2)(x+2)(x^2+4)`$ + +## $`10(3x-5)^4(2x+3)^5 + 4x^2(3x-5)^3(2x+6)^6`$ +- $`=(2x+3)^5(3x-5)^3(10(3x-5) + 4x^2(2x+3))`$ +- $`=(2x+3)^5(3x-5)^3(30x+50+8x^3+12x^2)`$ +- $`=(2x+3)^5(3x-5)^3(2(4x^3+6x^2+ 15x -25))`$ \ No newline at end of file