Polynomial Factoring

Factoring Polynomials Using Identities


Which of the following must be a factor of

x3+8? x^3 + 8 ?

Note: a3+b3=(a+b)(a2ab+b2). a^3 + b^3 = ( a + b ) ( a^2 - ab + b^2 ) .

Using the identity a2b2=(ab)(a+b) a^2 - b^2 = (a-b) ( a+b) , which of the following must be a factor of

x4+2500? x^4 + 2500 ?

If aa and bb are positive numbers and x438x2y2+y4=(x2+axyy2)(x2bxyy2),x^4-38x^2y^2+y^4=(x^2+axy-y^2)(x^2-bxy-y^2), what is the value of a+ba+b?

Suppose aa, bb, cc and dd are all non-positive integers such that the following is an algebraic identity in xx: (xa)2(x+a)2=x4+bx3+cx2+dx+256.(x-a)^2(x+a)^2=x^4+bx^3+cx^2+dx+256. What is the value of abcd-a-b-c-d?

Which of the following is a factor of x481x^4 - 81?


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