highschool/Grade 10/Math/MPM2DZ/Factoring Quiz.md

Level 1

\(`2x^4 - 32`\)

• \(`= 2(x^4-16)`\)
• \(`= 2((x^2-4)(x^2+4)`\)
• \(`= 2((x+2)(x-2)(x^2+4)) \\`\)

\(`2x^2+11x-21`\)

• \(`=2x^2+11x-21`\)
• \(`\quad \quad 2 \quad -3`\)
• \(`\quad \quad 1 \quad \quad 7`\)
• \(` = (2x+3)(x+7)`\)

\(`x^3y^2 + 2x^2y^2-3xy^2`\)

• \(`=xy^2(x^2+2x-3)`\)
• \(`\quad \quad \quad \quad 1 \quad -1`\)
• \(`\quad \quad \quad \quad 1 \quad \quad 3`\)
• \(`= xy^2(x-1)(x+3)`\)

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

\(`x^8 - 17x^4 - 48`\)

• \(`\text{Let } y = x^4`\)
• \(`= y^2 - 13y - 48`\)
• \(`\quad \quad 1 \quad \quad 3`\)
• \(`\quad \quad 1 \quad -16`\)
• \(`=(y+3)(y-16)`\)
• \(`=(x^4+3)(x^4-16)`\)
• \(`=(x^4+3)(x^2-4)(x^2+4)`\)
• \(`=(x^4+3)(x-2)(x+2)(x^2+4)`\)

\(`10(3x-5)^4(2x+3)^5 + 4x^2(3x-5)^3(2x+6)^6`\)

• \(`=(2x+3)^5(3x-5)^3(10(3x-5) + 4x^2(2x+3))`\)
• \(`=(2x+3)^5(3x-5)^3(30x+50+8x^3+12x^2)`\)
• \(`=(2x+3)^5(3x-5)^3(2(4x^3+6x^2+ 15x -25))`\)