Polynomial Factoring

Factoring Cubic Polynomials


What real value of xx satisfies the equation x321x2+20xx1=100? \frac{x^3-21x^2+20x}{x-1}= -100?

The cubic equation x37x2x+7=0x^3-7x^2-x+7=0 has three real roots. Let AA be the greatest root and BB be the least root. What is the value of ABA-B?

Given 2x3+17x2+19x14=(2xa)(x+b)(x+c),2x^3+17x^2+19x-14=(2x-a)(x+b)(x+c), what is the value of a+b+ca+b+c?

The polynomial in two variables

P(x,y)=x310y2+10x2y3 P(x,y) = x^3 - 10 y^2 + 10 x^2 - y^3

can be expressed as

P(x,y)=(ax+by+c)(dx2+exy+fy2+gx+hy+i), P(x,y) = (ax+by+c)(dx^2+exy + fy^2 + gx + hy + i ),

where the variables from aa to ii are all integers. What is the value of d+e+f+g+h+i | d + e + f + g + h + i | ?

If a,b,a,b, and cc are positive numbers such that x36x237x30=(x+a)(x+b)(xc),x^3-6x^2-37x-30=(x+a)(x+b)(x-c), what is the value of a+b+ca+b+c?


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