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A factored polynomial reveals its roots, a key concept in understanding the behavior of these expressions.

Factorize \[(x+2y)(x+2y+2)-8.\]

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Factorize \[(x+1)(x+2)(x-14)(x-15)+28.\]

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Which of the following is not a factor of \[x^4-2(4a^2+9b^2)x^2+(4a^2-9b^2)^2 ?\]

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Factorize \[(x^2-3x)^2-25x^2+75x-84.\]

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Factorize \[3(x-3)^2-4(x-3)(x+4)+(x+4)^2.\]

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