CT 13: Polynomials – I

1.The expression x² + 2xy + y² - a² + 2ab - b² has one factor as :

2. One of the factors of (x⁴ - 7x³ + 5x² + 31x - 30) is-

3. What is the coefficient of x when 8(x⁴ + 2x³ - 15x²) is divided by 4x(x + 5) ? 

4. What must be added to the polynomial f(x) = x⁴ + 2x³ - 2x² + x - 1 so that the resulting polynomial is exactly divisible by x² + 2x - 3?

5. Find the value of ‘k’, if x² − 2x + 1 is a factor of 2x⁴ + x³ − 14x² + 5k + 6.

6. For what value of k, is the polynomial f(x) = 3x⁴ - 9x³ + x² + 15x + k completely divisible by 3x² - 5?

7. If (x - 1)3 is a factor of x⁴ + αx3 +  βx2 + γx - 1, then the other factor will be:

8. What is the coefficient of x2 in the product of (x2 + 3x + 7) and (2x2 - 3x - 4)?

9. If α,β,γ are the zeros of the polynomial p(γ) = y³ - 2y² - y + 2, then

10. A factor of the expression x³ - 2x + 1 is: