Find factorization of `x^2 + (a+1/a)x + 1`

Solve by factorization: x^2+(a+1/a)x+1=0

If x= 2 is a factor of x^2+ ax + b and a +b =1. find the values of a and b.

If x-2 is a factor of x^2+3a x-2a, then a= (a) 2 (b) -2 (c) 1 (d) -1

Solve by factorization: 1/(x-2)+2/(x-1)=6/x ,\ \ x!=0

Find the coefficient of x^2 in (a/(a+x))^(1//2)+(a/(a-x))^(1//2)

Solve by factorization: 48 x^2-13 x-1=0

If (x + 1) and (x - 2) are factors of x^(3)+ (a + 1)x^2 -(b - 2) x-6, find the values of a and b. And then, factorise the given expression completely.

Solve the following quadratic equations by factorization method: 1/(x-2)+2/(x-1)=6/x

Solve by factorization: a(x^2+1)-x(a^2+1)=0