List of top Quantitative Aptitude Questions on Polynomials

If \( x^4 - x^3 + 2x^2 + ax + b \) is exactly divisible by \( x^2 - 3x + 2 \), then \( (a, b) \) is
The product of two expressions is x3+x2y-xy2-y3 and their HCF is (x+y). The LCM of those expressions will be :
If \( (x - a) \) is a factor of \( x^6 - ax^5 + x^4 - ax^3 + 3x - a + 2 \), then the value of \( a \) is:
Consider the curves: \[ y = 2x^3 + 3x^2 + 4, y = 3x^2 - 2x + 8 \] How many times do they intersect for \( -3 \leq x \leq 2 \)?
Suppose \(n\) is an integer such that the sum of digits of \(n\) is 2, and \(10^n<n<10^{n+1}\). The number of different values of \(n\) is
If \(f(x) = x^3 - 4x + p\), and \(f(0)\) and \(f(1)\) are of opposite signs, then which of the following is necessarily true?
If (Ax + By - Cz)2 = 4x2+ 3y2+ 2z2+ \(4\sqrt{3xy} \)-\( 2\sqrt{6yz}\) - 4√2xz, then find the value of A2+ B2C2.