Practice Problems

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I. State the coefficients and degrees of the polynomials. 1. 10x5 2. - 2.51 x4 3. - 8 4. 3 x2 II. Find the value of monomial when x = 3, 4. 1. 2x2 III. Find the values of the monomials when x = 2, 3, - 1.5 1. 3x2 2. -1.2 x2 3. 1/2x3 4. 2x3 IV. Simplify 1. ( - 3x )2 + ( 6x2 ) - ( -0.5x2 ) + ( 1 + 5x2) 2. ( - 3x ) + ( - 4x ) - ( 4.5 ) x + ( 2.5x ) 3. ( 3x ) + ( - 4x ) - ( - 3x ) + ( - 7x ) 4. ( - 5x2 ) + ( 5.2x2 ) + ( 1.5x2 ) - ( 0.7x2 ) 5. ( 3x3 - 4 x2 + 5 ) - ( 2 x3- 2 x2 + 3 ) 6. ( 3x3 - 2x2 - 3x - 3 ) - ( x3- 2 x2 + 3x - 4 ) 7. ( 7x5 - 6x4 + 5x3- 4x2 + 3x - 2 ) 8. If A = 3x3 + 4x2 - x - 1   B = 4 x3 - 3 x2+ 4x + 5   C = - 2 x3+ x2 - 5x + 4 Find B+C, C+B, (A+B) + C, A+ (B+ C), (A+C) +B Answers to Practice Problems. I. State the coefficients and degrees of the polynomials. 1. 10x5 Coefficient = 10; degree = 5 2. - 2.51 x4 Coefficient = -2.51; degree = 4 3. - 8 Coefficient = - 8; degree = 0 4. 3 x2 Coefficient = 3 ; degree = 2 II. Find the value of monomial when x = 3 , 4. 1. 2x2 when x = 3 2 · (2)3 = 16 When x = 4 2 · (2) 4 = 32. III. Find the values of the monomials when x = 2,3, -1.5 1. 3x2 When x = 2, the value of 3x2 = 3 · (2)2 = 12 When x = 3; the value of 3x2 = 3 · (3)2= 27 When x = - 1.5, the value of 3x2 = 3 · (-1.5)2 = 6.75 2. -1.2 x2 When x = 2, the value of -1.2 x2 =-1.2 · (2)2 = 4.8 When x = 3, the value of -1.2 x2 = -1.2 · (3)2= - 10.8 When x = - 1. 5 the value of -1. 2x2 = - 1.2 · ( - 1.5 )2 = - 2.7 3. 1/2 x3 When x = 2, the value of ½ x3 = ½ · 2 · 2 · 2 = 4 When x = 3 ; the value of ½ x3 = ½ · 3 · 3 · 3 = 13.5 When x = -1.5 the value of ½ x3 = ½ · -1.5 · -1.5 · -1.5 = -1.6875 4. 2x3 When x = 2, then the value of 2x3 = 2 · (2)3 = 2 · 8 = 16 When x = 3; then the value of 2x3 = 2 · (3)3 = 2 · 27 = 54 When x = - 1.5, then the value of 2x3 = 2 · (-1.5)3 = - 6.75 IV. Simplify 1. ( - 3x )2 + ( 6x2 ) - ( -0.5x2 ) + ( 1+ 5x2 ) = - 3x2 + 6x2 + 0.5x2 + 1.5x2 = ( - 3 + 6 + 0.5 + 1.5 ) x2 = 5x2 2. ( - 3x ) + ( - 4x ) - ( 4.5 ) x + ( 2.5x ) = ( - 3 - 4 - 4.5 + 2.5 ) x = - 9x 3. ( 3x ) + ( - 4x ) - (- 3x ) + ( - 7x ) = 3x - 4x + 3x - 7x = (3 - 4 + 3 - 7) x = - 5x 4. ( - 5x2 ) + ( 5.2x2 ) + ( 1.5x2 ) - ( 0.7x2 ) = ( - 5 + 5.2 + 1.5 - 0.7 ) x2 = ( 6.7 - 5.7 ) x2 = (1) x2 = x2 .5 ( 3x3 - 4x2+ 5 ) - ( 2x3- 2x2 + 3 ) = 3x3 - 4x2 + 5 - 2x3 + 2x2 - 3 = x3- 2x2 + 2. 6. ( 3x3 - 2x2 - 3x - 3 ) - ( x3- 2x2 + 3x - 4 ) = 3x3 - 2x2- 3x - 3 - x3+ 2x2 - 3x + 4 = 2x3 - 6x + 1. 7. ( 7x5 - 6x4 + 5x3- 4x2 + 3x - 2 ) - ( 2x5 -2x4 + x3 - x2 + x - 5 ) = 7x5 - 6x4 + 5x3- 4x2 + 3x - 2 - 2 x5 + 2 x4 - x3 + x2 - x + 5 = 5x5 - 4x4 + 4 x3 - 3 x2+ 2x + 3 8. If A = 3x3 + 4x2 - x - 1 B = 4x3 - 3x2+ 4x + 5 C = - 2 x3+ x2 - 5x + 4 B+C = ( 4x3 - 3x2+ 4x + 5 ) + ( - 2x3+ x2 - 5x + 4 )         = (4x3 - 2x3 ) + ( - 3x2+ x2 ) + ( 4x - 5x ) + 5 + 4         = 2x3 - 2x2- x + 9 C+B = ( - 2x3 + x2 - 5x + 4) + ( 4x3 - 3x2 + 4x + 5 )         = ( - 2 x3 + 4x3 ) + ( x2 - 3x2 ) + ( - 5x + 4x ) + 4+ 5         = 2x3 - 2x2 - x + 9 (A + B) + C = ( 7x3 + x2+ 3x + 4) + ( - 2x3+ x2- 5x + 4 )                   = 5 x3 + 2x - 2 x2+ 8 A+ ( B + C ) = ( 3 x3 + 4 x2- x - 1) + (2 x3- 2 x2-x + 9)                    = 5x3 + 2x2 - 2x + 8 A + C = x3+ 5x2 - 6x + 3 (A + C) + B = ( x3+ 5x2 - 6x + 3 ) + ( 4 x3 - 3x2 + 4x + 5 )                   = 5x3+ 2x2 - 2x + 8. redcomet.org - © 1999