Mathematics
If (2x + 1) is a factor of both the expressions 2x2 - 5x + p and 2x2 + 5x + q, find the values of p and q. Hence, find the other factors of both the polynomials.
Related Questions
If x3 - 2x2 + px + q has a factor (x + 2) and leaves a remainder 9 when divided by (x + 1), find the values of p and q. With these values of p and q, factorise the given polynomial completely.
If (x + 3) and (x - 4) are factors of x3 + ax2 - bx + 24, find the values of a and b. With these values of a and b, factorise the given expression.
If a polynomial f(x) = x4 - 2x3 + 3x2 - ax - b leaves remainders 5 and 19 when divided by (x - 1) and (x + 1) respectively, find the values of a and b. Hence, determine the remainder when f(x) is divided by (x - 2).
When a polynomial f(x) is divided by (x - 1), the remainder is 5 and when it is, divided by (x - 2), the remainder is 7. Find the remainder when it is divided by (x - 1)(x - 2).