Factorize the expressions of the form `ax^2+bx+c, \ a ne 1`

If (x-2)^(2) is the factor of an expression of the form x^(3)+bx+c , then the other factor is ______.

Factoris the expression. ax ^(3) - bx ^(2) + cx

If (x+2) is a common factor of the expression x^(2) + ax - 6, x^(2) + bx +2 and kx^(2) - ax - (a+b) , then k= "_____" .

If alpha and beta are the roots of the equation ax^(2) + bx + c = 0 , then what is the value of the expression (alpha + 1)(beta + 1) ?

Let a, b, c be three distinct real numbers such that each of the expressions ax^+bx +c, bx^2 + cx + a and ax^2 + bx + c are positive for all x in R and let alpha=(bc +ca+ab)/(a^2+b^2+c^2) then (A)alpha 1/4 (D) alpha>1

Given 4a-2b+c=0 where a,b,c in R, which of the following statement is/are not true in general? 1. (x+2) will always be a factor of the expression 2. (x-2) will always be a factor of the expression ax^(2) + bx + c. 3. There will always be a factor of the expression ax^(2) + bx+ c " different from" (x+2) Select the correct answer using the code given below:

The ratio of the roots of the equation ax^(2)+bx+c=0 is same equation Ax^(2)+Bx+C=0. If D_(1) and D_(2) are the discriminants of 0. If D_(1) and D_(2) are the ax^(2)+bx+C=0 and Ax^(2)+Bx+C=0 respectively,then D_(1):D_(2)