Name: Class: Date: ID: A Alg B Chapter 7 Final Exam Review Please answer all questions and show your work. Simplify ( 2) 4. 2. Simplify ( 4) 4. 3. Simplify 5 2. 4. Simplify 9x0 y 3 z 8. 5. Simplify 7w0 r 8 t 7. 6. Simplify 8w0 r 2 t 5. 7. Simplify (x 2 ) 6 x 2.
Name: ID: A 8. Simplify (x 5 ) 8 x 4. 9. Simplify (x 4 ) 7 x 2. 0. Simplify b 3 p 6 (bp) 2.. Simplify a 8 b 9 (ab) 3. 2. Simplify y5 z 8 (yz) 2. 3. Find the degree of the polynomial 9x 4 y 5 + 2xy + x 2. 4. Find the degree of the polynomial 2x 2 y 6 + 4.5xy + x 2. 5. Find the degree of the polynomial 5x 2 y 5 + 3.5xy + x 4. 2
Name: ID: A 6. Write the polynomial 7x 3 + 3 + 4x 4 + x 2 5x 5 5x in standard form. Then give the leading coefficient. 7. Write the polynomial 8x 2 + 4x 4x 5 0x 3 + 9x 4 + 8 in standard form. Then give the leading coefficient. 8. Write the polynomial 9x 3 + 5 5x 5 3x 2 3x 4 7x in standard form. Then give the leading coefficient. 9. Add. (2b 5 b 2 ) + (b 5 + 4b 2 3) 20. Add. (6d 5 d 3 ) + (d 5 + 5d 3 ) 2. Add. (7e 3 e ) + (e 3 + 3e ) 22. Subtract. (7e 5 e 3 ) (e 5 + 4e 3 2) 23. Subtract. (0e 3 e ) (e 3 + 6e 2) 3
Name: ID: A 24. Subtract. (3c 4 c ) (c 4 + 6c ) 25. Multiply. (x )(x 3) 26. Multiply. (2m + )(m 2) 27. Multiply. (x + 5)(x + ) 28. Multiply. (x 2) 2 29. Multiply. (p 3) 2 30. Multiply. (z 7) 2 4
Alg B Chapter 7 Final Exam Review Answer Section SHORT ANSWER. ANS: 6 ( 2) 4 = ( 2) 4 The reciprocal of 2 is ( 2). = 6 ( 2) 4 = 6. PTS: DIF: Average REF: Page 447 OBJ: 7-.2 Zero and Negative Exponents NAT: 2...d TOP: 7- Integer Exponents KEY: negative exponent evaluate power exponent 2. ANS: 256 ( 4) 4 = ( 4) 4 The reciprocal of 4 is ( 4). = 256 ( 4) 4 = 256. PTS: DIF: Average REF: Page 447 OBJ: 7-.2 Zero and Negative Exponents NAT: 2...d TOP: 7- Integer Exponents KEY: negative exponent evaluate power exponent 3. ANS: 25 5 2 = 5 2 The reciprocal of 5 is 5. = 25 5 2 = 25. PTS: DIF: Average REF: Page 447 OBJ: 7-.2 Zero and Negative Exponents NAT: 2...d TOP: 7- Integer Exponents KEY: negative exponent evaluate power exponent
4. ANS: 9z 8 y 3 9x 0 y 3 z 8 = 9 y 3 = 9 = 9 = 9z8 y 3 z 8 y 3 z 8 y 3 z8 z 8 = z8. 9x 0 y 3 Rewrite z 8 without negative or zero exponents. Simplify each part of the expression. y 3 = y 3. PTS: DIF: Advanced REF: Page 448 OBJ: 7-.4 Simplify Expressions with Zero and Negative Exponents NAT: 2.5.3.d TOP: 7- Integer Exponents 5. ANS: 7t 7 r 8 7w 0 r 8 t 7 = 7 r 8 = 7 = 7 = 7t7 r 8 r 8 t 7 t 7 7w 0 r 8 Rewrite t 7 without negative or zero exponents. Simplify each part of the expression. r 8 = r 8. r 8 t7 t 7 = t7. PTS: DIF: Advanced REF: Page 448 OBJ: 7-.4 Simplify Expressions with Zero and Negative Exponents NAT: 2.5.3.d TOP: 7- Integer Exponents 2
6. ANS: 8t 5 r 2 8w 0 r 2 t 5 = 8 r 2 = 8 = 8 = 8t5 r 2 t 5 r 2 t 5 8w 0 r 2 Rewrite t 5 without negative or zero exponents. Simplify each part of the expression. r 2 = r 2. r 2 t5 t 5 = t5. PTS: DIF: Advanced REF: Page 448 OBJ: 7-.4 Simplify Expressions with Zero and Negative Exponents NAT: 2.5.3.d TOP: 7- Integer Exponents 7. ANS: x 0 (x 2 ) 6 x 2 x 2 6) x 2 Use the Power of a Power Property. x 2 x 2 Simplify the exponent of the first term. x 2 + 2 Add the exponents since the powers have the same base. x 0 x 0 Write with a positive exponent. PTS: DIF: Advanced REF: Page 462 OBJ: 7-3.3 Finding Powers of Powers NAT: 2.5.3.c TOP: 7-3 Multiplication Properties of Exponents 3
8. ANS: x 36 (x 5 ) 8 x 4 x 5 8) x 4 Use the Power of a Power Property. x 40 x 4 Simplify the exponent of the first term. x 40 + 4 Add the exponents since the powers have the same base. x 36 x 36 Write with a positive exponent. PTS: DIF: Advanced REF: Page 462 OBJ: 7-3.3 Finding Powers of Powers NAT: 2.5.3.c TOP: 7-3 Multiplication Properties of Exponents 9. ANS: x 26 (x 4 ) 7 x 2 x 4 7) x 2 Use the Power of a Power Property. x 28 x 2 Simplify the exponent of the first term. x 28 + 2 Add the exponents since the powers have the same base. x 26 x 26 Write with a positive exponent. PTS: DIF: Advanced REF: Page 462 OBJ: 7-3.3 Finding Powers of Powers NAT: 2.5.3.c TOP: 7-3 Multiplication Properties of Exponents 0. ANS: b p 4 First, use the Power of a Product Property to rewrite the denominator. Then, for each power with the same base, keep the base and subtract the exponents. PTS: DIF: Average REF: Page 467 OBJ: 7-4. Finding Quotients of Powers NAT: 2.5.3.c TOP: 7-4 Division Properties of Exponents KEY: exponent power division base 4
. ANS: a 5 b 6 First, use the Power of a Product Property to rewrite the denominator. Then, for each power with the same base, keep the base and subtract the exponents. PTS: DIF: Average REF: Page 467 OBJ: 7-4. Finding Quotients of Powers NAT: 2.5.3.c TOP: 7-4 Division Properties of Exponents KEY: exponent power division base 2. ANS: y 3 z 6 First, use the Power of a Product Property to rewrite the denominator. Then, for each power with the same base, keep the base and subtract the exponents. PTS: DIF: Average REF: Page 467 OBJ: 7-4. Finding Quotients of Powers NAT: 2.5.3.c TOP: 7-4 Division Properties of Exponents KEY: exponent power division base 3. ANS: 9 9x 4 y 5 : degree 9, 2xy: degree 2, and x 2 : degree 2 The degree of the polynomial is 9. PTS: DIF: Average REF: Page 476 OBJ: 7-5.2 Finding the Degree of a Polynomial TOP: 7-5 Polynomials 4. ANS: 8 2x 2 y 6 : degree 8, 4.5xy: degree 2, and x 2 : degree 2 The degree of the polynomial is 8. PTS: DIF: Average REF: Page 476 OBJ: 7-5.2 Finding the Degree of a Polynomial TOP: 7-5 Polynomials 5. ANS: 7 5x 2 y 5 : degree 7, 3.5xy: degree 2, and x 4 : degree 4 The degree of the polynomial is 7. PTS: DIF: Average REF: Page 476 OBJ: 7-5.2 Finding the Degree of a Polynomial TOP: 7-5 Polynomials NAT: 2.5.2.b NAT: 2.5.2.b NAT: 2.5.2.b 5
6. ANS: 5x 5 + 4x 4 + 7x 3 + x 2 5x + 3 The leading coefficient is 5. The standard form is written with the terms in order from highest to lowest degree. PTS: DIF: Basic REF: Page 477 OBJ: 7-5.3 Writing Polynomials in Standard Form TOP: 7-5 Polynomials 7. ANS: NAT: 2.5.3.d 4x 5 + 9x 4 0x 3 + 8x 2 + 4x + 8 The leading coefficient is 4. The standard form is written with the terms in order from highest to lowest degree. PTS: DIF: Basic REF: Page 477 OBJ: 7-5.3 Writing Polynomials in Standard Form TOP: 7-5 Polynomials 8. ANS: NAT: 2.5.3.d 5x 5 3x 4 9x 3 3x 2 7x + 5 The leading coefficient is 5. The standard form is written with the terms in order from highest to lowest degree. PTS: DIF: Basic REF: Page 477 OBJ: 7-5.3 Writing Polynomials in Standard Form TOP: 7-5 Polynomials 9. ANS: 3b 5 + 3b 2 3 (2b 5 b 2 ) + (b 5 + 4b 2 3) = (2b 5 + 4b 2 ) + ( b 2 + b 5 ) + ( 3) = 3b 5 + 3b 2 3 NAT: 2.5.3.d Identify like terms. Rearrange terms to get like terms together. Combine like terms. PTS: DIF: Basic REF: Page 485 OBJ: 7-6.2 Adding Polynomials NAT: 2.5.3.c TOP: 7-6 Adding and Subtracting Polynomials 20. ANS: 7d 5 + 4d 3 (6d 5 d 3 ) + (d 5 + 5d 3 ) = (6d 5 + 5d 3 ) + ( d 3 + d 5 ) + ( ) = 7d 5 + 4d 3 Identify like terms. Rearrange terms to get like terms together. Combine like terms. PTS: DIF: Basic REF: Page 485 OBJ: 7-6.2 Adding Polynomials NAT: 2.5.3.c TOP: 7-6 Adding and Subtracting Polynomials 6
2. ANS: 8e 3 + 2e (7e 3 e ) + (e 3 + 3e ) = (7e 3 + 3e ) + ( e + e 3 ) + ( ) = 8e 3 + 2e Identify like terms. Rearrange terms to get like terms together. Combine like terms. PTS: DIF: Basic REF: Page 485 OBJ: 7-6.2 Adding Polynomials NAT: 2.5.3.c TOP: 7-6 Adding and Subtracting Polynomials 22. ANS: 6e 5 5e 3 + 2 (7e 5 e 3 ) (e 5 + 4e 3 2) = (7e 5 e 3 ) + ( e 5 4e 3 + 2) = (7e 5 e 5 ) + ( e 3 4e 3 ) + ( 2) = 6e 5 5e 3 + 2 Rewrite subtraction as addition of the opposite. Identify like terms. Rearrange terms to get like terms together. Combine like terms. PTS: DIF: Average REF: Page 485 OBJ: 7-6.3 Subtracting Polynomials NAT: 2.5.3.c TOP: 7-6 Adding and Subtracting Polynomials 23. ANS: 9e 3 7e + 2 (0e 3 e ) (e 3 + 6e 2) = (0e 3 e ) + ( e 3 6e + 2) = (0e 3 e 3 ) + ( e 6e ) + ( 2) = 9e 3 7e + 2 Rewrite subtraction as addition of the opposite. Identify like terms. Rearrange terms to get like terms together. Combine like terms. PTS: DIF: Average REF: Page 485 OBJ: 7-6.3 Subtracting Polynomials NAT: 2.5.3.c TOP: 7-6 Adding and Subtracting Polynomials 7
24. ANS: 2c 4 7c + (3c 4 c ) (c 4 + 6c ) = (3c 4 c ) + ( c 4 6c + ) = (3c 4 c 4 ) + ( c 6c ) + ( ) = 2c 4 7c + Rewrite subtraction as addition of the opposite. Identify like terms. Rearrange terms to get like terms together. Combine like terms. PTS: DIF: Average REF: Page 485 OBJ: 7-6.3 Subtracting Polynomials NAT: 2.5.3.c TOP: 7-6 Adding and Subtracting Polynomials 25. ANS: x 2 4x + 3 (x )(x 3) Use FOIL. x(x 3) (x 3) Distribute x and. x(x) + x( 3) (x) ( 3) Distribute x and again. x 2 3x x + 3 Multiply. x 2 4x + 3 Combine like-terms. PTS: DIF: Basic REF: Page 494 OBJ: 7-7.3 Multiplying Binomials NAT: 2.5.3.c TOP: 7-7 Multiplying Polynomials 26. ANS: m 2 m 2 (m + )(m 2) Use FOIL. m(m 2) + (m 2) Distribute m and. m(m) + m( 2) + (m) + ( 2) Distribute m and again. m 2 2m + m 2 Multiply. m 2 m 2 Combine like-terms. PTS: DIF: Basic REF: Page 494 OBJ: 7-7.3 Multiplying Binomials NAT: 2.5.3.c TOP: 7-7 Multiplying Polynomials 8
27. ANS: x 2 + 6x + 5 (x + 5)(x + ) Use FOIL. x(x + ) + 5(x + ) Distribute x and 5. x(x) + x(+) + 5(x) + 5(+) Distribute x and 5 again. x 2 + x + 5x + 5 Multiply. x 2 + 6x + 5 Combine like-terms. PTS: DIF: Basic REF: Page 494 OBJ: 7-7.3 Multiplying Binomials NAT: 2.5.3.c TOP: 7-7 Multiplying Polynomials 28. ANS: x 2 4x + 4 (x 2) 2 ( a b) = a 2 2ab + b 2 Use the rule for ( a b). (x 2) 2 = x 2 2(x)(2) + 2 2 Use the FOIL method, and then combine like terms. x 2 4x + 4 Simplify. PTS: DIF: Basic REF: Page 502 OBJ: 7-8.2 Finding Products in the Form (a b)2 TOP: 7-8 Special Products of Binomials 29. ANS: p 2 6p + 9 (p 3) 2 NAT: 2.5.3.c ( a b) = a 2 2ab + b 2 Use the rule for ( a b). (p 3) 2 = p 2 2(p)(3) + 3 2 Use the FOIL method, and then combine like terms. p 2 6p + 9 Simplify. PTS: DIF: Basic REF: Page 502 OBJ: 7-8.2 Finding Products in the Form (a b)2 TOP: 7-8 Special Products of Binomials NAT: 2.5.3.c 9
30. ANS: z 2 4z + 49 (z 7) 2 ( a b) = a 2 2ab + b 2 Use the rule for ( a b). (z 7) 2 = z 2 2(z)(7) + 7 2 Use the FOIL method, and then combine like terms. z 2 4z + 49 Simplify. PTS: DIF: Basic REF: Page 502 OBJ: 7-8.2 Finding Products in the Form (a b)2 TOP: 7-8 Special Products of Binomials NAT: 2.5.3.c 0