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1 Chap 2 : Polynomials all GUIDE and Sample Paper PDFs by whatsapp from +91 89056 29969 Page 9 CHAPTER CHAPTER 22 Polynomials1. OBJECTIVE QUESTIONS1. Factors of xx1242-- are(a) ,,xxx22 32+-+^^^hh h(b) ,,xxx33 22+-+^^^hh h(c) ,,xxx22 32+--^^^hh h(d) ,xx2622+-^^hhAns : (a) ,,xxx22 32+-+^^^hh hWe can find two numbers p and q such that qp1+=-and pq12= numbers are 4- and 3. xx1242-- xxx4312422=-+- xxx43 4222=-+ -^^hh xx4322=-+^^hh xxx22 32=+-+^^^hhh2. If xxxyx11222-=++bl, then the value of y is(a) 2- (b) 2(c) x2 (d) x2-Ans : (a) 2-3. x abcxabbc2+++ ++=^h(a) xaxbc+++^^hh (b) xaxac+++^^hh(c) xbxac+++^^hh (d) xbxbc+++^^hhAns : (c) xbxac+++^^hhx abcxabbc2+++ ++^h xacxbxbac2=++ ++ +^^hh xbxacxb2=+++ +^^hh xx ba c x b=+++ +^^^hhh xbxac=+++^^hh4. Factorisation of abxx22- is(a) ababxxxx+-^^hh (b) abxx2-^h(c) ababxx22+-^^hh (d) ababxx22-+^^hhAns : (a) ababxxxx+-^^hh abxx22- abxx22=-^^hh ababxxxx=+-^^hh5.

2 Which one of the following algebraic expressions is a polynomial in variable x?(a) xx222+ (b) xx1+(c) xxx3/232+ (d) None of theseAns : (c) xxx3/232+xxx3/232+ can be written as xx32+, which is a polynomial in If one factor of xx58 42+- is ()x21+, then the second factor is(a) ()x52+ (b) ()x25-(c) ()x52- (d) ()x52-+Ans : (c) ()x52-7. Degree of the polynomial px^hxx3674=++ 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 If one factor of ()a x y zbx 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+Add 89056 29969 in Your Class Whatsapp Group to Get All PDF Degree of the polynomial pxxx22=+-^^ ^hhh is(a) 2 (b) 1(c) 0 (d) 3 Ans : (a) 2 px^h xx22=+-^^hh x42=-The highest power of the variable x is 2.

3 So the degree of the polynomial, ()px2=10. If xx88742-+ is divided by x21+, the remainder is(a) 211 (b) 213(c) 215 (d) 217 Ans : (a) 211 Let, px^h xx88742=-+So, the remainder when px^h is divided by x21+ is p21-bl 821821742=---+bbll 211=11. If abc0++=, then abc333++=(a) abc (b) abc3(c) abc2 (d) abc3-File Revision date : 20 September 2019 Objective QuestionsCLASS : 9 th SUB : Maths For NCERT Solutions Previous Years Chapterwise QB visit or whatsapp at 8905629969 Download all GUIDE and Sample Paper pdfs from or Page 10 Chap 2 : Polynomials Ans : (b) abc3We know that,abc abc3333++- abca b c abbcca222=++ ++- - -^^hhIf abc++ 0=, then abc333++ abc3=.12. For the polynomial pxxxx x451532=+-+-^h, one of the factors is(a) x1+^h (b) x1-^h(c) x (d) x2+^hAns : (b) x1-^h px^h xxxx451532=+-+- p1^h 14511=+-+- 0=Hence, x1= is the solution of px^ In the method of factorisation of an algebraic expression, which of the following statement is false?

4 (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 : (c) Using remainder theorem is not used for factorisation of an algebraic If x2=, y1=-, then the value of xxyy4422++ is(a) 0 (b) 1(c) 1- (d) 2 Ans : (a) 015. Factorisation of ab abbcca222++ ++^h is(a) abab c2+++^^hh (b) bcca b2+++^^hh(c) caab c2+++^^hh (d) babc a2+++^^hhAns : (a) abab c2+++^^hhab abbcca222++ ++^h ab ab bcca2222=++ + +^h ab cab22++ +^^hh abab c2=+++^^hh16. Factors ofzyxzyx36 1131232+-+--+aakk()zyxzyx43449532+-+- +-+bl are(a) ()xzyx143449--+-bl(b) ()xzyx143449+-+-bl(c) ()xzyx143449-++-bl(d) ()xzyx143449++++blAns : (a) ()xzyx143449--+-bl17. If x2=- and xy xy3522++=-, then find (a) 2- (b) 3(c) 4- (d) 9 Ans : (b) 3 Value of xy xy322++ 5=- and x2=- yy2622-+-^h 5=- yy692-+ 0= y32-^h 0= y3- 0= y 3=Download All PDF fi les from Expansion of xx12+bl is(a) xxx2122++ (b) xxx2122-+(c) xx2122++ (d) xx2122-+Ans : (c) xx2122++19.

5 Factors of polynomial xx x3102432--+ are(a) ()()()xxx234-+- (b) ()()()xxx234+++(c) ()()()xxx234+-- (d) ()()()xxx234---Ans : (a) ()()()xxx234-+-20. If xx15+=, then find the value of xx122+(a) 26 (b) 23(c) 30 (d) 22 Ans : (b) 23 xx1+ 5= xx12+bl 52=^h xxxx21122++^bbhll 25= xx2122++ 25=or xx122+ 23=21. Factorisation of xx32 42++ is (a) xx222++^^hh (b) xx222+-^^hh(c) xx222-+^^hh (d) xx222--^^hhAns : (a) xx222++^^hh xx32 42++ xxx222 42=+++ xxx222 22=+++^^hh xx222=++^^hh22. The values of a and b so that the polynomial xax xb1332--+ is divisible by ()x1+ and ()x3- are(a) ,ab153== (b) ,ab012==-(c) ,ab315=-= (d) ,ab120=-=Chap 2 : Polynomials all GUIDE and Sample Paper PDFs by whatsapp from +91 89056 29969 Page 11 Ans : (b) ,ab012==-23. Factorisation of xaa1222-- - is(a) xa xa11-- +-^^hh (b) xa xa11++ --^^hh(c) xa xa11++ -+^^hh (d) xa xa11-+ +-^^hhAns : (b) xa xa11++ --^^hh xaa1222-- - xaa1222=-++^h xa122=-+^h xa xa11=++ --^^hh24.

6 Factors of ababa2-+ - are(a) ()()aba1-+ (b) ()()aba1+-(c) ()()aba1-- (d) ()()aba1++Ans : (b) ()()aba1+-25. Which of the following algebraic expressions is not a polynomial ?(a) xx21732+- (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 xx422--^h are(a) ,xx76--^^hh (b) ,xx76+-^^hh(c) ,xx76+-^^hh (d) ,xx76-+^^hhAns : (c) ,xx76+-^^hh xx422-- xxx42 762=-+- xx x766=-+ -^^hh xx67=-+^^hhDownload All PDF fi les from The polynomials axx3322+- and xxa253-+ when divided by ()x4- leaves remainders R1 and R2 respectively, then value of a if RR2012-=, is(a) 12718- (b) 3218(c) 12717 (d) 3117-Ans : (b) 321828. Factors of ab ab33+--^^hh are(a) ,abab2322+^h (b) ,abab322+^h(c) ,ba b2322+^h (d) ,ab a3222+^hAns : (c) ,ba b2322+^hab ab33+--^^hh ab ab ab ab2=+-- +++^^^ ^hhh h78A ab ab2-+-^^hhB ba abbaba abb222222222=+ ++-+- +6@ ba If ()()xxxkx4262--=++, then the value of k is(a) 6 (b) 6-(c) 7 (d) 7-Ans : (d) 7-30.

7 The common quantity that must be added to each term of :ab22 to make it equal to :ab is(a) ab (b) ab+(c) ab- (d) baAns : (a) abConsider :ab22,Adding ab on both sides, we get :aabbab22++^^hh :aa b ba b=++^^hh:ab=.31. Factors of xx7122-+ are(a) ()()xx34-+ (b) ()()xx34--(c) ()()xx34+- (d) ()()xx34++Ans : (b) ()()xx34--32. One of the dimensions of the cuboid whose volume is xx1626102-+ is(a) 2 (b) x85-^h(c) x1-^h (d) All of theseAns : (d) All of these xx1626102-+ xx2 81352=-+^h xxx288 5 52=--+^h xx28 51=--^^hh33. Find the value of xyz++ if xyz18222++= and xy yz zx9++=(a) 9 (b) 3(c) 6 (d) 8 Ans : (c) 6 xyz2++^h xyz xy yz zx222222=+++ + + 18 2 9=+^h 36= xyz++ 6=34. Find the remainder when the polynomial fx^hxxx345032=-++ is divided by x3+(a) 16- (b) 12-(c) 20- (d) 10-Ans : (a) 16-x3=- is the zero of x3+.

8 By the remainder theorem, we know that when fx^h is divided by x3+^h, the remainder is f3-^ , f3-^h 33 34 35022##=-- -+ -+]^^ghh8B 27 27 12 50=---+^h 16=-35. If ()()x xy y xayx ybxy231023222+- ++-=++ --, then the values of a and b are(a) 11 and 5 (b) 1 and 5-(c) 1- and 5- (d) 11- and 5 Ans : (d) 11- and 5 Download all GUIDE and Sample Paper pdfs from or Page 12 Chap 2 : Polynomials 36. The value of a for which xa+^h is a factor of the polynomial xax xa2632+-++ is(a) 4 (b) 2(c) 4- (d) 2-Ans : (d) 2-xa+^h is a factor of fx^h xax xa2632=+-++ fa-^h 0= xax a0&+==-6@aaaaa2632-+---++^^^hhh 0= a3 6=- a 2=-37. Factorisation of the polynomial xx311632++ is(a) xx32 33+-^^hh (b) xx32 33++^^hh(c) xx23 23++^^hh (d) xx22 32-+^^hhAns : (b) xx32 33++^^hh xx311632++ xxx3 92632=+++ xxx333233=+++^^hh xx32 33=++^^hhAdd 89056 29969 in Your Class Whatsapp Group to Get All PDF Find the value of xy xy83621633-- -, when xy26=+(a) 1- (b) 2(c) 0 (d) 3 Ans : (c) 0We have, xy xy83621633-- - xyxy26326333=+- +- - - -^^^^^hhhhh xy x yxy yx26436 212622=-- +++ - +^^hh xyxy yx0436212622#=+++-+^h 0= xyxy26260&=+--=^h2.

9 FILL IN THE BLANKDIRECTION : Complete the following statements with an appropriate word/term to be filled in the blank space(s).1. xa- is a factor of the polynomial ()px, if ()pa= ..Ans : 02. The degree of the polynomial xy z73102 is ..Ans : 153. Factors of xy66- is ..Ans : ()()()()xyxyxyxyxyxy2222-++- ++4. A polynomial of degree one is called a .. : linear5. A polynomial of degree three is called a .. : cubic6. The factors of abx abc3333++- are ..Ans : ()()abca b c abbcca222++ ++- - -7. A polynomial of one term is called a ..Ans : monomial8. The quotient of xxx87532-+ when divided by x2 is ..Ans : xx427252-+9. A polynomial of three terms is called a ..Ans : trinomial10. The remainder obtained when xxx80552017232+++ is divided by x2+ is ..Ans : 288-11. xxx118814234-+ is called a .. : biquadratic12. If abc0++=, then abc333++= ..Ans : abc abc3333++=3. TRUE/FALSEDIRECTION : Read the following statements and write your answer as true or The number of zeroes of a polynomial is the degree of the : True2.

10 Xxx542332-++ is a polynomial over : True3. A polynomial may have more than one : True4. xx3562-+ is a polynomial of degree : True5. ()()xxxx31163 33322++=++Ans : True6. xx x73 2532-+ + is a : True7. Every polynomial is a : FalseChap 2 : Polynomials all GUIDE and Sample Paper PDFs by whatsapp from +91 89056 29969 Page 138. When xxx69732-++ is divided by ()x1- remainder is : True9. Every binomial is a polynomial of degree : False10. The degree of a constant polynomial is : FalseDownload All PDF fi les from MATCHING QUESTIONSDIRECTION : In the section, each question has two matching lists. Choices for the correct combination of elements from Column-I and Column-II are given as options (a), (b), (c) and (d) out of which one is Column-II shows the degree of polynomials given Column-IColumn-IColumn-II(P)yy y2223 8--+(1) 2(Q) 2(2) 1(R)x57-(3) 0(S)x42-(4) 8 PQRS(a)1324(b)4321(c)4231(d)2341 Ans : P - 4, Q - 3, R - 2, S - 1(P) The highest power of the variable is 8.