Algebra Worksheet-1

Algebra Worksheet-1

1. Which of the following expressions is a polynomial?

(a)                                (b)

(c) 3x²y –2xy + 5x⁴                      (d)

2. The degree of the polynomial 5x³ – 6x³y + 4y² – 8 is:

(a) 3                                                 (b) 4

(c) 2                                                 (d) can’t be determined

3. What must be added to x³ + 3x – 8 to get 3x³ + x² + 6?

(a) 2x³ + x² – 3x + 14                  (b) 2x² + x² + 14

(c) 2x³ + x² – 6x – 14                  (d) None of these

4. What must be subtracted from x³ – 3x² + 5x – 1 to get 2x³ + x² + 4x + 2?

(a) –x³ + 4x² – 9x + 3                 (b) x³ + 4x² – 9x + 3

(c) x³ – 4x² + 9x – 3                    (d) –x³ – 4x² + 9x – 3

5. Divide (–56 mnp²) by (7 mnp).

(a) –8p               (b) 8 mnp          (c) 8 p                 (d) None of these

6. A factor of x³ – 1 is:

(a) x – 1                                          (b) x² + x + 1

(c) either A or B                            (d) None of these

7. The product of by is:

(a)             (b) x²yz               (c) 6x²yz             (d) None of these

8. Divide 8x²y² – 6xy² + 10x²y³ by 2xy.

(a) 4xy – 3y + 5xy²                       (b) 4xy + 3y – 5xy²

(c) 8xy + 3y – 5xy²                       (d) 4xy – 3y – 5xy²

9. The product of (x² + 3x + 5) and (x² – 1) is:

(a) x⁴ + 3x³ – 4x² – 3x – 5         (b) x⁴ + 3x³ + 4x² – 3x – 5

(c) x⁴ + 3x³ + 4x² + 3x – 5         (d) None of these

10. If quotient = 3x² – 2x + 1, remainder = 2x – 5 and divisor = x + 2 then the divided is:

(a) 3x³ – 4x² + –3                        (b) 3x³ – 4x² – x + 3

(c) 3x³ + 4x² – x + 3                    (d) 3x³ + 4x² – x – 3

11. If (x – 2) is one factor of x² + ax – 6 = 0 and x² – 9x + b = 0 then a + b = ______.

(a) 15                  (b) 13                  (c) 11                   (d) 10

12. The remainder obtained when t⁶ + 3t² + 10 is divided by t³ + 1 is:

(a) t² – 11           (b) t³ – 1             (c) 3t³ + 11         (d) None of these

13. The value of the product (3x² – 5x + 6) and (–8x³) when x = 0 is:

(a)                    (b) 2                    (c) 1                     (d) 0

14. The difference of the degree of the polynomials 3x²y³ + 5xy⁷ – x⁶ and 3x⁵ – 4x³ + 2 is:

(a) 2                    (b) 3                    (c) 1                     (d) None of these

15. What must be added to x² + 5x – 6 to get x³ – x² + 3x – 2?

(a) x³ – 2x² – 2x – 4                    (b) x³ + 2x² – 2x + 4

(c) x³ – 2x² – 2x + 4                    (d) None of these

Answer Key:

(1)-c; (2)-b; (3)-a; (4)-d; (5)-a; (6)-c; (7)-b; (8)-a; (9)-b; (10)-d; (11)-a; (12)-c; (13)-d; (14)-b; (15)-c