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57 lines
1.4 KiB
Markdown
57 lines
1.4 KiB
Markdown
# Level 1
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## $`2x^4 - 32`$
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- $`= 2(x^4-16)`$
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- $`= 2((x^2-4)(x^2+4)`$
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- $`= 2((x+2)(x-2)(x^2+4)) \\`$
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## $`2x^2+11x-21`$
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- $`=2x^2+11x-21`$
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- $`\quad \quad 2 \quad -3`$
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- $`\quad \quad 1 \quad \quad 7`$
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- $` = (2x+3)(x+7)`$
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## $`x^3y^2 + 2x^2y^2-3xy^2`$
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- $`=xy^2(x^2+2x-3)`$
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- $`\quad \quad \quad \quad 1 \quad -1`$
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- $`\quad \quad \quad \quad 1 \quad \quad 3`$
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- $`= xy^2(x-1)(x+3)`$
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# Level 2
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## $`4x^4-9x^2+30x-25`$
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- $`=4x^4-(9x^2-30x+25)`$
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- $`\quad \quad \quad \quad \quad \quad 3 \quad -5`$
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- $`\quad \quad \quad \quad \quad \quad 3 \quad -5`$
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- $`= 4x^4 - (3x-5)^2`$
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- $`= (2x^2-3x+5)(2x^2+3x-5)`$
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- $`\quad \quad \quad \quad \quad \quad \quad \quad \quad 2 \quad \quad 5`$
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- $`\quad \quad \quad \quad \quad \quad \quad \quad \quad 1 \quad -1`$
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- $` = (2x^2-3x+5)(2x+5)(x-1)`$
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## $`3(x-y)^2 - 5x + 5y - 2`$
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- $`= 3(x-y)^2 -5(x-y) - 2`$
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- $`\text{Let } a = (x-y)`$
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- $`= 3a^2 - 5a - 2`$
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- $` \quad \quad 3 \quad \quad 1`$
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- $` \quad \quad 1 \quad -2 `$
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- $`= (3a+1)(a-2)`$
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- $`=(3(x-y)+1)(x-y-2)`$
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- $`=(3x-3y+1)(x-y-2)`$
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# Level 3
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## $`x^8 - 17x^4 - 48`$
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- $`\text{Let } y = x^4`$
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- $`= y^2 - 13y - 48`$
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- $`\quad \quad 1 \quad \quad 3`$
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- $`\quad \quad 1 \quad -16`$
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- $`=(y+3)(y-16)`$
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- $`=(x^4+3)(x^4-16)`$
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- $`=(x^4+3)(x^2-4)(x^2+4)`$
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- $`=(x^4+3)(x-2)(x+2)(x^2+4)`$
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## $`10(3x-5)^4(2x+3)^5 + 4x^2(3x-5)^3(2x+6)^6`$
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- $`=(2x+3)^5(3x-5)^3(10(3x-5) + 4x^2(2x+3))`$
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- $`=(2x+3)^5(3x-5)^3(30x+50+8x^3+12x^2)`$
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- $`=(2x+3)^5(3x-5)^3(2(4x^3+6x^2+ 15x -25))`$ |