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Chap 2 : Polynomials www.rava.org.in

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CHAPTER CHAPTER 22

1. OBJECTIVE QUESTIONS

1. Factors of xx12

42
are (a) ,,xxx22 3 2 ^^^hh h (b) ,,xxx33 2 2 ^^^hh h (c) ,,xxx22 3 2 ^^^hh h (d) ,xx26 22
^^hh

Ans : (a) ,,xxx22 3

2 ^^^hh h

We can find two numbers p and q such that

qp1and pq12.

The numbers are

4 and 3.

xx12 42
xxx4312 422
xx x43 4 22 2
^^hh xx43 22
^^hh xxx22 3 2 ^^^hhh 2. If xxxyx1 1 22
2 bl, then the value of y is (a)

2 (b) 2

(c) x2 (d) x2

Ans : (a) 23. x abcxabbc

2 ^h (a) xaxbc^^hh (b) xaxac^^hh (c) xbxac^^hh (d) xbxbc^^hh

Ans : (c) xbxac^^hh

x abcxabbc 2 ^h xacxbxbac 2 ^^hh xbxacxb 2 ^^hh xx b a c x b ^^^hhh xbxac^^hh

4. Factorisation of ab

xx22 is (a) abab xxxx ^^hh (b) ab xx2 ^h (c) abab xx22 ^^hh (d) abab xx22 ^^hh

Ans : (a) abab

xxxx ^^hh ab xx22 ab xx22 ^^hh abab xxxx ^^hh

5. Which one of the following algebraic expressions is a

polynomial in variable x? (a) xx2 2 2 (b) xx1(c) xxx3 /232 (d) None of these

Ans : (c) xxx3

/232 xxx3 /232 can be written as xx3 2 , which is a polynomial in x.

6. If one factor of

xx58 4 2 is ()x

21, then the

second factor is (a) ()x52 (b) ()x25 (c) ()x52 (d) ()x52

Ans : (c) ()x52

7. Degree of the polynomial px^hxx367

4 is (a) 4 (b) 5 (c) 3 (d) 1

Ans : (a) 4

The highest power of the variable

x is 4. So, the degree of the polynomial is 4.

8. If one factor of

()a x y z bx by bz is (),xyz then the second factor is (a) ax ay az (b) bx by bz (c) bx by bz (d) ab

Ans : (d) ab

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9. Degree of the polynomial px x x22^^ ^hhh is

(a) 2 (b) 1 (c) 0 (d) 3

Ans : (a) 2

px^h xx22^^hh x4 2 The highest power of the variable x is 2. So the degree of the polynomial, ()px2

10. If xx887

42
is divided by x21, the remainder is (a) 211
(b) 213
(c) 215
(d) 217

Ans : (a)

211

Let, px^h xx887

42

So, the remainder when px^h is divided by x21 is

p21bl 8218217 42
bbll 211

11. If abc0, then abc

333
(a) abc (b) abc3 (c) abc2 (d) abc3

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Ans : (b) abc3

We know that,

abc abc3 333
abca b c abbcca 222
^^hh

If abc 0, then abc

333
abc3.

12. For the polynomial px x x x x45 1

532
^h, one of the factors is (a) x1 ^h (b) x1^h (c) x (d) x2^h

Ans : (b) x1^h

px^h xxxx45 1 532
p1 ^h 14511 0

Hence,

x1 is the solution of px ^h.

13. In the method of factorisation of an algebraic

expression, which of the following statement is false? (a) Taking out a common factor from two or more terms. (b) Taking out a common factor from a group of terms. (c) Using remainder theorem. (d) Using standard identities.

Ans : (c) Using remainder theorem.

Remainder theorem is not used for factorisation of an algebraic expression.

14. If x2, y1, then the value of xxyy44

22
is (a) 0 (b) 1 (c)

1 (d) 2

Ans : (a) 0

15. Factorisation of ab abbcca2

22
^h is (a) abab c2 ^^hh (b) bcca b2^^hh (c) caab c2^^hh (d) babc a2^^hh

Ans : (a) abab c2^^hh

ab abbcca2 22
^h ab ab bcca22 22
^h ab cab2 2 ^^hh abab c2^^hh

16. Factors of

z yxzyx36 113123 2 aakk ()zyx zyx4344953 2 bl are (a) ()xzyx143449 bl (b) ()xzyx143449 bl (c) ()xzyx143449 bl (d) ()xzyx143449 bl

Ans : (a) ()xzyx143449

bl

17. If x2 and xy xy35

22
, then find (a)

2 (b) 3

(c)

4 (d) 9

Ans : (b) 3

Value of

xy xy3 22

5 and x2

yy26 22
^h 5 yy69 2 0 y3 2 ^h 0 y3 0 y 3

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18. Expansion of xx1

2 bl is (a) xxx21 2 2 (b) xxx21 2 2 (c) xx21 2 2 (d) xx21 2 2

Ans : (c) xx21

2 2

19. Factors of polynomial xx x31024

32
are (a) ()()()xxx234 (b) ()()()xxx234 (c) ()()()xxx234 (d) ()()()xxx234

Ans : (a) ()()()xxx234

20. If xx15

, then find the value of xx1 2 2 (a) 26 (b) 23 (c) 30 (d) 22

Ans : (b) 23

xx1 5 xx1 2 bl 5 2 ^h xxxx211 22
^bbhll 25
xx21 2 2 25
or xx1 2 2 23

21. Factorisation of xx32 4

2 is (a) xx22 2 ^^hh (b) xx22 2^^hh (c) xx22 2^^hh (d) xx22 2^^hh

Ans : (a) xx22 2^^hh

xx32 4 2 xxx22 2 4 2 xx x22 2 22^^hh xx22 2^^hh

22. The values of a and b so that the polynomial

xax xb13 32
is divisible by ()x1 and ()x3 are (a) ,ab15 3 (b) ,ab012 (c) ,ab315 (d) ,ab12 0

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Ans : (b) ,ab012

23. Factorisation of xaa12

22
is (a) xa xa11 ^^hh (b) xa xa11 ^^hh (c) xa xa11 ^^hh (d) xa xa11 ^^hh

Ans : (b) xa xa11 ^^hh

xaa12 22
xaa12 22
^h xa1 22
^h xa xa11 ^^hh

24. Factors of ababa

2 are (a) ()()aba1 (b) ()()aba1 (c) ()()aba1 (d) ()()aba1

Ans : (b) ()()aba1

25. Which of the following algebraic expressions is not a

polynomial ? (a) xx2173 2 (b) xx73 8 /323 (c) 3 (d) 0

Ans : (b) xx73 8

/323

The expression xx73 8

/323 is not a polynomial as second term has fractional exponent /23

26. Factors of xx42

2 ^h are (a) ,xx76 ^^hh (b) ,xx76^^hh (c) ,xx76^^hh (d) ,xx76^^hh

Ans : (c) ,xx76^^hh

xx42 2 xxx42 7 6 2 xx x76 6 ^^hh xx67^^hh

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27. The polynomials ax x33

quotesdbs_dbs21.pdfusesText_27

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