CT 19: Polynomials – I

1.The remainder on dividing the polynomial x2 - 2x + 1 by (x-1) will be:

2. Which of the following cannot be a zero of the polynomial x³ - x² - 6x?

3. What should be subtracted from x⁴ + x³ - 2x² + x + 1 such that it is divisible by x – 1?

4. If one of the zeroes of the cubic polynomial x³ + ax² + bx + c is -1 then the product of the other two zeroes is:

5. Find the degree of the polynomial:

2x³ - 3x² + 5x + 2 = 0

6. Find the remainder when f(x) = 3x³ - 5x² + 2x + 8 is divided by g(x) = 2x - 1.

7. Find the cubic polynomial when the zeroes  are 3, -1, −1/2

8. If the two zeros of the polynomial x3 + x2 - 7x - 7 are √7 and -√7, then the third zero will be:

9. If x + a is a factor of x⁴ - a²x² + 3x - 6a, then a =

10. If the polynomial f(x) = 2x³ - kx² + 5x + 9 is exactly divisible by x + 2, then k =