Polynomials

If x^2 + 1/x^2 = 7, find x + 1/x (for positive x).

The HCF of two polynomials is (x-3) and their LCM is x^2-9. If one polynomial is x^2-9, find the other.

Find the remainder when x^5 is divided by x-1.

What is the sum of coefficients in (x-y)^2?

Factorize x^3 - 7x + 6.

If x^2 + x + 1 = 0, find x^3.

Find the value of (a-b)^3 + (b-c)^3 + (c-a)^3.

If x+y+z=6 and x^2+y^2+z^2=14, find xy+yz+zx.

Factorize 2x^2 + 7x + 3.

What is the HCF of a^3b - ab^3 and a^2b - ab^2?

Simplify (x+2)^3 - (x-2)^3.

Find the remainder when x^4 + x^3 + x^2 + x + 1 is divided by x.

If x-2 is a factor of x^2 + ax - 6, find a.

Expand (a+b+c)^2.

Find the degree of 0x^5 + 3x^4 - x + 2.

What is the root of the polynomial P(x) = 7x - 14?