Ws7 Polynomial

Date:

______/______/ 2009

Marks

Worksheet 7: Simplifying Algebraic Expressions (Polynomials) 1

Basic Question Simplify the following expressions (a) 3 x + ( −4 x) + 2 = − x + 2 (b) 2 x 2 − x + 3 x 2 + 4 x = 5 x 2 + 3 x (c) x 2 − x 2 − x 2 = − x 2

2

Intermediate Question Simplify the following expressions (a) 4 x − 2 + x 2 − 3 x + 6 = x 2 + x + 4 (b) 3 x + 2 x 2 − 5 x − 4 x 2 = −2 x 2 − 2 x (c) 2 x 2 + 3 x − x 2 + 5 − 2 x − 4 = x 2 + x + 1 (d) xy + 3 xy + 6 x 2 − 3 x 2 + 3 = 4 xy + 3 x 2 + 3

3

Intermediate Question Simplify the following expressions (a) (−5 x 2 − 8 x − 2) + (3 x 2 − x − 5) = −2 x 2 − 9 x − 7 (b) ( 2 x 2 + xy + 3 y 2 ) + ( x 2 + 2 xy − y 2 ) = 3 x 2 + 3 xy + 2 y 2 (c) ( 3 x 2 − 8 x + 5 ) − ( x 2 − 3 x + 2 ) = 2 x 2 − 5 x + 3 (d) ( 2 x 2 − 5 xy + 3 y 2 ) − ( x 2 + 2 xy + y 2 ) = x 2 − 7 xy + 2 y 2

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4

Intermediate Question Subtract (a) a 4 + 4a 2 + 7 from 5a 5 + 2a 4 − 3a 3 + 2a 2 − 9 . (b) 2a 5 − 3a 4 + 7 a 3 − 6 from 7 a 5 + 4a 4 − 2a 3 + 3a + 2 . (a)5a 5 + 2a 4 − 3a 3 + 2a 2 − 9 − ( a 4 + 4a 2 + 7 ) = 5a 5 + 2a 4 − 3a 3 + 2a 2 − 9 − a 4 − 4a 2 − 7 = 5a 5 + a 4 − 3a 3 − 2a 2 − 16 (b)7 a 5 + 4a 4 − 2a 3 + 3a + 2 − ( 2a 5 − 3a 4 + 7 a 3 − 6 ) = 7 a 5 + 4a 4 − 2a 3 + 3a + 2 − 2a 5 + 3a 4 − 7 a 3 + 6 = 5a 5 + 7 a 4 − 9a 3 + 3a + 8

5

Advance Question Find the polynomial which must be subtracted from 2 x 3 + x 2 + 1 to get x 4 + 3x 3 + 2 x 2 + x . Let the polynomial be a.

2 x3 + x 2 + 1 − a = x 4 + 3x3 + 2 x 2 + x ∴ a = 2 x3 + x 2 + 1 − ( x 4 + 3 x 3 + 2 x 2 + x ) = 2 x3 + x 2 + 1 − x 4 − 3x3 − 2 x 2 − x = − x 4 − x3 − x 2 − x + 1 The polynomial is − x 4 − x 3 − x 2 − x + 1

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