Find the values of `p\ a n d\ q` so that `x^4+p x^3+2x^2-3x+q` is divisible by `(x^2-1)`

Find the values of a\ a n d\ b so that (x+1)a n d\ (x-1) are factors of x^4+a x^3-3x^2+2x+b

Find the values of p and q , so that f(x)={{:(x^(2)+3x+p, ifxle1),(qx+2,ifx gt1):} is differentiable at x = 1

Let P(x) and Q(x) be two polynomials.Suppose that f(x) = P(x^3) + x Q(x^3) is divisible by x^2 + x+1, then (a) P(x) is divisible by (x-1),but Q(x) is not divisible by x -1 (b) Q(x) is divisible by (x-1), but P(x) is not divisible by x-1 (c) Both P(x) and Q(x) are divisible by x-1 (d) f(x) is divisible by x-1

The polynomial px^(3)+4x^(2)-3x+q completely divisible by x^2-1: find the values of p and q. Also for these values of p and q factorize the given polynomial completely.

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

Find the values of p and q for which the following system of equations has infinite number of solutions: 2x+3y=7,\ \ \ \ (p+q)x+(2p-q)y=21

Find the values of p and q for which the following system of equations has infinite number of solutions: 2x+3y=7,\ \ \ \ (p+q)x+(2p-q)y=21

Let P(x) and Q(x) be two polynomials. If f(x) = P(x^4) + xQ(x^4) is divisible by x^2 + 1 , then

Let p be the statement "x is divisible b, 4" and q be the statement "x is divisible by 2". STATEMENT-1 : p hArr q and STATEMENT-2 : If x is divisible by 4, it must be divisible by 2 .

Prove that x^(3p) + x^(3q+1) + x^(3r+2) is exactly divisible by x^2+x+1 , if p,q,r is integer.