Algebra

Polynomial Factoring

Factoring Compound Quadratics

         

If aa, bb, cc and dd are positive numbers that satisfy x440x2+4=(x2+axb)(x2cxd),x^4-40x^2+4 = (x^2+ax-b)(x^2-cx-d), what is the value of a+b+c+da+b+c+d?

If aa and bb are positive numbers such that x3+2x2y9x18y=(x+a)(xb)(x+cy),x^3+2x^2y-9x-18y=(x+a)(x-b)(x+cy), what is the value of a+b+ca+b+c?

If bb and cc are positive numbers such that (x21)(x2+8x+7)=(x+a)2(x+b)(xc),(x^2-1)(x^2+8x+7)=(x+a)^2(x+b)(x-c), what is the value of a+b+ca+b+c?

If aa and bb are positive integers such that x2y29x2z210xy2+90xz2+25y2225z2=(xa)2(ybz)(y+bz),\begin{aligned} & x^2 y^2-9x^2z^2-10xy^2+90xz^2+25y^2-225z^2\\ & =(x-a)^2(y-bz)(y+bz), \end{aligned} what is the value of a+ba+b?

A polynomial x4226x2+225x^4-226x^2+225 can be factorized as (xa)(xb)(xc)(xd).(x-a)(x-b)(x-c)(x-d). If the four constants satisfy a<b<c<da < b < c < d, what is the value of bcadbc-ad?

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