8 more about polynomials ii 2 3 1 2 2 2 x 7 x 15 x 3x

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Unformatted text preview: +1 ÷ ×2 2 3 x + x +1 6 − 6x 3x − 27 Solution x 3x 5x + + (5 x − 1)(3 x − 2) (3 x − 2)( x + 3) (1 − 5 x )( x + 3) Solution 7 NSS Mathematics in Action Worksheets 4B 6. 8 More about Polynomials (II) 2 3 1 +2 −2 2 x − 7 x − 15 x − 3x − 10 2 x + 7 x + 6 2 Solution 7. x2 y − 3x x 1 × + ÷ 2 2 2 9x + 3y x 9x − y Solution 8. (a) Prove that a + 2 is a factor of 2a 3 − 9a 2 − 11a + 30 . (b) Factorize 2a 3 − 9a 2 − 11a + 30 completely. (c) Hence, simplify a 2 − 10a + 25 a2 − 4 . ×2 2a 3 − 9a 2 − 11a + 30 a − 7a + 10 Solution (a) (b) (c) 8 NSS Mathematics in Action Worksheets 4B 8 More about Polynomials (II) Solutions 8 More about Polynomials (II) L.C.M. Worksheet 8.1 (Basic) a 3b = a 3 × b 1. a 5b 2 = a 5 × b 2 = a3 × b ∴ H.C.F. = a 3b = a5 × b 2 L.C.M. 2. = a 5b 2 a 3b 2c = a 3 × b 2 × c a 2b 4 c 3 = a 2 × b 4 × c 3 ∴ = a 2 × b2 × c H.C.F. = a 2b 2 c = a 3 × b 4 × c3 L.C.M. 3. = a 3b 4c 3 12 x 4 y 8 = 2 2 × 3 45 x 6 y 3 = ∴ 32 × 5 × x 6 × y 3 H.C.F. = 3 × x4 × y3 = 3x 4 y 3 L.C.M. 4. × x4 × y8 15 x 2 yz 7 = = 2 2 × 32 × 5 × x 6 × y 8 = 180 x 6 y 8 3 × 5 × x2 × y × z 7 24 y 2 z 4 = 23 × 3 × y2 × z4 4 ∴ H.C.F. = 3 × y × z = 3 yz 4 L.C.M. 5. 9ab3c 5 = = 23 × 3 × 5 × x 2 × y 2 × z 7 = 120 x 2 y 2 z 7 32 30b 4c 2 = 2 × 3 × 5 45a 3c 4 = ∴ H.C.F. × a × b3 × c 5 × b4 × c2 32 × 5 × a 3 × c4 = 3× c 2 = 3c 2 9 = 2 × 32 × 5 × a 3 × b 4 × c 5 = 90a 3b 4 c 5 NSS Mathematics in Action Worksheets 4B 6. 8 More about Polynomials (II) 3a 2 (b − 2) = 3 × a 2 × (b − 2) 9(b − 2)3 = 32 ∴ H.C.F. × (b − 2)3 = 3 × (b − 2) = 3(b − 2) 2 2 3 L.C.M. = 3 × a × (b − 2) 2 3 = 9a (b − 2) 7. ( a − b )3 ( a + b 2 ) = ( a − b )3 × ( a + b 2 ) ( a − b) 2 (a + 2b) = ( a − b) 2 ∴ H.C.F. = ( a − b) 2 L.C.M. 8. = ( a − b) 3 ( a + b 2 )(a + 2b) 4 x 2 ( x + y )(2 x − y ) = 2 2 × x 2 × ( x + y ) × ( 2 x − y ) 16( x + y ) 3 ( 2 x − y ) 2 = 2 4 ∴ H.C.F. × ( x + y ) 3 × (2 x − y) 2 = 2 2 × ( x + y ) × (2 x − y ) = 4( x + y )(2 x − y ) L.C.M. 9. × (...
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