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Polynomial Factoring

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

Factoring Polynomials

         

Completely factorize \[x^3-3x^2+4x-12.\]

Find the sum of all real solutions of the equation \[x^2-36=3(x-6)^2.\]

Completely factorize \[x^4+15x^3+70x^2+120x+64.\]

If \(f(x)=x^3-(3+a)x^2+(2+3a)x-2a\) and \(g(x)=x^3+4x^2+8x+8\) share a common factor, what is the value of \(a?\)

If the complete factorization of \(x^3-1x^2-26x-24\) gives \[(x+a)(x+b)(x+c),\] what is the value of \(abc?\)

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