Simplify the given expression.

​$$x^2 + 3x + 12 - 2(x^3 - x + 4)$$​​​

The sum of squares of all the roots of the equation:
​$$\left(x + \frac{1}{x}\right)^2 - 4 = \frac{3}{2} \left(x - \frac{1}{x}\right), x \neq 0$$ is:

What is the remainder when the polynomial x¹⁰⁰ – 2x⁵¹ + 1 is divided by (x² – 1) ?

Solution of $$\dfrac{x - 2}{x + 5} > 2$$​ is:

​$$\text{Sum and product of all roots of } 4x^3 - 8x^2 - 13x + 19 = 0 \text{ is:}$$​

If x² + y² − 10x + 26y + 194 = 0, then the value of x² + y² is:

If the polynomial ax³ + 4x² + 3x − 4 and x³ – 7x + a leaves the same remainder, when divided by (x − 2), then find the value of a.​

Factorise the polynomial $$x^4 - 10x^2 + 22$$​ into product of two quadratic polynomials.

the LCM and HCF of polynomial P(x) and Q(x) are $$56(x^4 + x)$$ and $$4(x^2 -x + 1)$$, respectively. If the polynomial P(x) = $$28(x^3 + 1),$$ then Q(x) is equal to​

If x = 110,y = 111, z = 112, then find the value of $$x^3+y^3+z^3-3xyz$$​.

Find the values of k for which x$$^2$$​ + 5kx + k$$^2$$​ + 5 is exactly divisible by x + 2 but not divisible by x + 3.