Factorize the following polynmials:
(1) `x^(2)-4x-5`
`=x^(2)-5x+x-5`
`=x(x-5)+1(x-5)`
`=(x-5)(x+1)`

Factorize the following expressions x^2+5x+x+5

Factorize the following: 2a(4x-1)+5(4x-1)

x ^ (2) -4x-5 = (x-5) (x + 1)

Determine whether (x-1) is a factor of the following polynomials: (i) x ^(3) +5x^(2) -10 x +4 (ii) x^(4) +5x^(2) -5x + 1

Factorize the following expressions (5x-1/x)^2+4(5x-1/x)+4,xne0

Factorize each of the following expressions: x^(4)+x^(2)+1 (ii) x^(4)+5x^(2)+9

Factorize each of the following expressions : x^4+x^2+1 (ii) x^4+5x^2+9

Find the LCM and HCF of the following polynomials 36(x +2)^(2) (x-1)^(3) (x +3)^(5), 45 (x +2)^(5) (x -1)^(2) (x +3)^(5) and 63 (x -1)^(5) (x +2)^(5) (x +3)^(4)

Check whether the following are quadratic equations : (1) (x-3)^(2)=x(2x-5) (2) (2x-3)(8x+1) = (4x+5)(4x-5) (3) (5x+3)(x-2)=(4x+3)(2x-1) (4) (2x+5)^(3)=8(x-1)^(3) (5) x^(2)+7x-8=x(x+5) (6) x^(3)+9x^(2)-7x+2=(x+3)^(3)