`( x+3) ` is a factor of p(x) , if p(_) =0

(3-x) is a factor of p(x) , if p(_) =0

(-x-b) is a factor of p(x) , if p(_) =0

(-x+b) is a factor of p(x) , if p(_) =0

If x - 3 is a factor of p(x) , then the remainder is

If (x+2) is a common factor of (px^2+qx+r) and (qx^2+px+r) then a) p=q or p+q+r=0 b) p=r or p+q+r=0 c) q=r or p+q+r=0 d) p=q=-1/2r

Find the value of p for which x+1 is a factor of x^4+(p-3)x^3-(3p-5)x^2+(2p-9)x+6. Find the remaining factor for this value of pdot

By remainder theorem , find the remainder when p(x) is divided by g(x) where , (i) p(x) =x^(3) -2x^2 -4x -1 ,g(x) =x+1 (ii) p(x) =4x^(3) -12x^(2) +14x -3,g(x) =2x-1 (iii) p(x) =x^(3) -3x^(2) +4x +50 ,g(x) =x-3

If 2 + isqrt3 is a root of x^(3) - 6x^(2) + px + q = 0 (where p and q are real) then p + q is