MCQ Class 10 Mathematics Polynomials Division Algorithm For Polynomials

1. There will be total 20  MCQ in this test.
2. Please keep a pen and paper ready for rough work but keep your books away.
3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number.
4. No negative marking for incorrect choice.
5. Please click on “Finish the Test” when you want to exit.
6. All the best – Happy Studying

1. The expression that should be subtracted from the polynomial f(x) = x⁴ + 2x³ -13x² - 12x + 21 so that the resulting polynomial is exactly divisible by g(x) = x² – 4x + 3 is

x² - 3

2x - 3

x - 4

x² + 4

Question 1 of 20

2. If (x + 1) is a factor of x² - 3ax + 3a - 7, then the value of a is:

-2

0

1

-1

Question 2 of 20

3. The value of quadratic polynomial f (x)=2x²- 3x- 2 at x =-2 is ……

12

15

-12

16

Question 3 of 20

4. If the degree of the dividend is 5 and the degree of the divisor is 3, then the degree of the quotient will be

2

1

-2

0

Question 4 of 20

5. value of ‘a’ so that (x + 6) is a factor of the polynomial x³ + 5x² - 4x + a.

10

0

13

12

Question 5 of 20

6. On dividing f(x) = x³ - 3x² + x + 2 by a polynomial g(x) the quotient and remainder q(x) and r(x) are (x – 2) and (-2x + 4) respectively, then g(x) is

x² + x - 3

x² - x + 1

2x² - 1 + x

x² + x - 1

Question 6 of 20

7. The three zeroes of the polynomial 2x³ + 5x² - 28x - 15 _____

All three are not real numbers

Are all Natural numbers

Are all rational numbers

Are all Integers

Question 7 of 20

8. If two of the zeroes of the polynomial f (x) = x⁴ - 3x³ - x² + 9x - 6 are -√3 and √3 then all the zeroes are

√3 , -√3 , 2 , 3

√3 , -√3 , 1 , 3

√3 , -√3 , 1, 2

-1 , 4 , √3 , -√3

Question 8 of 20

9. If (x + 1) is a factor of 2x³ + ax² + 2bx + 1, then find the values of a and b given that 2a - 3b = 4.

a = 2, b = 2

a = 5, b = 5

a = 2, b = 5

a = 5, b = 2

Question 9 of 20

10. Which of the given is the set of zeroes of the polynomial p(x) = 2x³ + x² - 5x + 2

1/2 , -1 , -2

1/2 , 1 , -2

-1/2 , -1 , -2

-1/2 , 1 , -2

Question 10 of 20

11. The value of p when x³ + 9x² + px - 10 is exactly divisible by (x+ 2 ) is ____

1

9

3

6

Question 11 of 20

12. When the polynomial f(x) = 4x³ + 8x² + 8x + 7 is divided by the polynomial g(x) = 2x² - x + 1, the quotient and the remainder are

Quotient = 2x + 5, Remainder = 11x + 2

Quotient = 2x - 5, Remainder = 11x

Quotient = x² - 5, Remainder = 15

Quotient = x -5, Remainder = 13

Question 12 of 20

13. When x² - 2x + k divides the polynomial x⁴ - 6x³ + 16x² - 25x + 10, the remainder is (x + a) . The value of a is __________

-3

3

-5

5

Question 13 of 20

14. If the degree of the divisor g(x) is one then the degree of the remainder r(x) is

3

2

0

1

Question 14 of 20

15. If the polynomial (2x + 3 ) is a factor of the polynomial
2x³ + 9x² - x – b. The value of b is_______

10

5

15

20

Question 15 of 20

16. If two of the zeros of the polynomial x⁴ - 17 x³ + 90 x² - 166 x + 92 are ( 7 + √3 ) and (7 - √3 ) , then the other two zeros are _________

2 and 3

( 7 + √3 ) and (7 - √3 )

1 and 2

7 and -7

Question 16 of 20

17. If f(x) is divided by g(x), g(x)  ≠ 0 , then there exist two polynomials q(x) and r(x) such that

r(x) = f(x) g(x) + q(x)

q(x) = f(x) g(x) - r(x)

g(x) = f(x) q (x) + r (x)

f(x) = g (x) q (x) + r (x)

Question 17 of 20

18. The expression that should be added to the polynomial f(x) = x⁴ + 2x³ – 2x² + x + 1, so that it should be exactly divisible by (x² + 2x – 3) is

x³ – 3

2 - x

x + 2

x - 4

Question 18 of 20

19. When x³ - 3x² + 5x - 3 is divided by x² - k , the remainder is 7x + a . Then the value of k is_____

1

2

6

3

Question 19 of 20

20. If two zeroes of a polynomial 4x⁴ -20x³ +23 x² + 5x - 6 are ½ and - ½ , the how many more zeroes does it have?

3

None

1

2

Question 20 of 20

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