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8-1 Study Guide and Intervention

12 +5 Not a Polynomial. 4.8g²h-78h+2 Yes Trinomial with degree 3. 6.6x+x² Yes. Two Adding and Subtracting Polynomials. Add and Subtract Polynomials To add ...



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Study Guide and Intervention (continued). Multiplying a Polynomial by a Monomial ... (4x-5)². 16x2. 40x + 25. Lesson 8-8. Example. Find (5x + 3y)(5x — $y). (a + b)( ...



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Study Guide and Intervention (continued). Adding and Subtracting Polynomials. PERIOD. Subtract Polynomials You can subtract a polynomial by adding its additive 



Chapter 8 Resource Masters

1 2 3 4 5 6 7 8 9 DOH 16 15 14 13 12 11. CONSUMABLE WORKBOOKS Many of the Study Guide and Intervention These masters provide vocabulary key concepts ...



Chapter 8 Resource Masters

1 2 3 4 5 6 7 8 9 DOH 16 15 14 13 12 11. CONSUMABLE WORKBOOKS Many of the Study Guide and Intervention These masters provide vocabulary key concepts ...



8-1 Study Guide and Intervention - Adding and Subtracting

Polynomials in Standard Form A polynomial is a monomial or a sum of monomials. A binomial is the sum of two monomials and a trinomial is the sum of three 



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To add or subtract polynomials perform the indicated operations and combine like terms. Study Guide and Intervention (continued). Dividing Polynomials. Use ...



Chapter 8 Resource Masters

Study Guide and Intervention Multiplying and Dividing Rational Expressions add and subtract rational expressions or to multiply and divide them. How can your.



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Page 8. 5-4 Study Guide and Intervention (continued). Analyzing Graphs of Polynomial Functions. Maximum and Minimum Points A quadratic function has either a 



Study Guide and Intervention Workbook

the difference of a number squared and 8 n2 - 8. The algebraic expression is n2 - 8. Step 4 Do all addition and/or subtraction from left to right. Evaluate ...



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8-1 Study Guide and Intervention (continued}. Multiplying Monomials Subtract Polynomials You can subtract a polynomial by adding its additive inverse.



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7-4 Study Guide and Intervention. Adding and Subtracting Polynomials. Add Polynomials To add polynomials you can group like terms horizontally or write.



Chapter 8 Resource Masters

Chapter 8. 5. Glencoe Algebra 1. Study Guide and Intervention. Adding and Subtracting Polynomials. Polynomials in Standard Form A polynomial is a monomial 



8-1 Study Guide and Intervention.pdf

8-1 Study Guide and Intervention. Adding and Subtracting Polynomials. Polynomials in Standard Form A polynomial is a monomial or a sum of monomials.



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8-1 Study Guide and Intervention. Adding and Subtracting Polynomials. Polynomials in Standard Form A polynomial is a monomial or a sum of monomials.



5-1 Study Guide and Intervention

5. Glencoe Algebra 2. 5-1 Study Guide and Intervention 8. m7 . m8 ... To add or subtract polynomials perform the indicated operations and combine like ...



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8-1. NAME. Study Guide and Intervention (continued). Multiplying Monomials Then give the degree of the polynomial. 5. 3. 7x. Expression. 9x3 + 4x +.



8-3 Study Guide and Intervention - Multiplying Polynomials

Chapter 8. 18. Glencoe Algebra 1. 8-3 Study Guide and Intervention. Multiplying Polynomials. Multiply Binomials To multiply two binomials you can apply the 



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5-1 Study Guide - Operations with Polynomials To add or subtract polynomials perform the indicated operations and combine like terms.



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Chapter 8. A2. Glencoe Algebra 1. NAME. DATE. PERIOD. PAANZA LED Quem. Study Guide and Intervention (continued). Adding and Subtracting Polynomials.



00i ALG1 A CRM C08 TP 660282 - Weebly

Adding and Subtracting Polynomials Find each sum or difference 1 (2 x + 3 y) (4 9 6x + 12y 2 (6 s+ 5 t) (4 8 14s + 9t 3 (5a + 9b) - (2a + 4b) 3a + 5b 4 (11m - 7n) - (2m + 6n) 9m - 13n 5 (m2-m) + (2m + m2) 2m2 + m 6 (x2 - 3x) - (2x2 + 5x) -x2 - 8x 7 (d2-d + 5) - (2d + 5) d 2 - 3d 8 (2h2 - 5h) + (7h - 3h2) -h + 2h 9 (5f + g - 2) + (-2f





8-1 Study Guide and Intervention - Waynesville R-Vi School

Adding and Subtracting Polynomials Polynomials in Standard Form A polynomial is a monomial or a sum of monomials A binomial is the sum of two monomials and a trinomial is the sum of three monomials Polynomials with more than three terms have no special name The degree of a monomial is the sum of the exponents of all its variables





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May 3 2010 · students before beginning Lesson 8-1 Encourage them to add these pages to their Algebra Study Notebook Remind them to add definitions and examples as they complete each lesson Study Guide and Intervention Each lesson in Algebra 1addresses two objectives There is one Study Guide and Intervention master for each objective WHEN TO USE Use

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Lesson X-1

NAME DATE PERIOD

Lesson 5-1

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Chapter 5 5 Glencoe Algebra 2

5-1Study Guide and Intervention

Operations with Polynomials

Exercises

Simplify. Assume that no variable equals 0.

1. c 12 c 4 c 6 2. b 8 b 2 3. (a 4 5 4. x 2 y x 4 y 1 5. a 2 b a 3 b 2 1 6. x 2 y xy 3 2 7. 1 2 (-5a 2 b 3 2 abc 2 8. m 7 . m 8 9. 8 m 3 n 2 4 mn 3 10. 2 3 c 4 t 2 2 2 c 4 t 2

11. 4j(-j

2 k 2 )(3 j 3 k 7 ) 12. 2 mn 2 ( 3m 2 n 2 12 m 3 n 4 a. (3m 4 n 2 5 mn 2 (3 m 4 n 2 5 mn 2 = 3m 4 n 2 25
m 2 n 2 = 75m 4 m 2 n-2 n 2 = 75m 4 2 n 2 2 = 75m 6 b. ( -m 4 3 ( 2m 2 2 ( -m 4 3 ( 2 m 2 2 m 12 1 4 m 4 = -m 12 . 4m 4 = -4m

16Product of Powersa

m . a n a m + n for any real number a and integers m and n

Quotient of Powers

a m a n = a m - n for any real number a ≠ 0 and integers m and n.

Properties of Powers

For a, b real numbers and m, n integers:

a m n = a mn ab m = a m b m a b n a n b n , b ≠ 0 a b n b a n or b n a n , a ≠ 0, b ≠ 0

Simplify. Assume that no variable equals 0.

Multiply and Divide Monomials Negative exponents are a way of expressing the multiplicative inverse of a number.

When you

simplify an expression , you rewrite it without powers of powers, parentheses, or negative exponents. Each base appears only once, and all fractions are in simplest form. The following properties are useful when simplifying expressions.Negative Exponents a n 1 a n and 1 a n = a n for any real number a ≠ 0 and any integer n.

Example

c 14 b 6 a 20 y 2 x 6 b a 5 x 2 y 4 25
2 a 6 b 8 c 2 m 15 2 m 2 n 2 12 j 2 k 5 3 2 m 2

001_020_ALG2_A_CRM_C05_CR_660789.indd 5

001_020_ALG2_A_CRM_C05_CR_660789.indd 512/20/10 9:12 PM12/20/10 9:12 PM

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NAME DATE PERIOD

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Chapter 5 6 Glencoe Algebra 2

5-1Study Guide and Intervention (continued)

Operations with Polynomials

Operations with Polynomials

To add or subtract polynomials, perform the indicated operations and combine like terms.

Simplify 4xy

2 + 12xy - 7x 2 y - (20xy + 5xy 2 - 8x 2 y 4 xy 2 + 12xy - 7x 2 y - (20xy + 5xy 2 - 8x 2 y = 4xy 2 + 12xy - 7x 2 y - 20xy - 5xy 2 + 8x 2 y

Distribute the minus sign.

= (-7x 2 y + 8x 2 y (4 xy 2 - 5xy 2 ) + (12xy - 20xy) Group like terms. = x 2 y - xy 2 - 8xy Combine like terms.

Polynomiala monomial or a sum of monomials

Like Termsterms that have the same variable(s) raised to the same power(s) You use the distributive property when you multiply polynomials. When multiplying binomials, the FOIL pattern is helpful.

Find (6x - 5)(2x + 1).

(6 x - 5)(2x + 1) = 6x

2x + 6x

1 + (-5)

2x + (-5)

1

First terms Outer terms Inner terms Last terms

= 12x 2 + 6x - 10x - 5 Multiply monomials. = 12x 2 - 4x - 5 Add like terms. FOIL PatternTo multiply two binomials, add the products of F the ? r s t terms, O the outer terms, I the inner terms, and L the last terms.

Find each product.

7. 2x(3x

2 - 5) 8. 7a(6 - 2a - a 2 9. (x 2 - 2)(x 2 - 5) 10. (x + 1)(2x 2 - 3x + 1)

11. (2n

2 - 3)(n 2 + 5n - 1) 12. (x - 1)(x 2 - 3x + 4)Simplify.

1. (6x

2 - 3x + 2) - (4x 2 + x - 3) 2. (7y 2 + 12xy - 5x 2 ) + (6xy - 4y 2 - 3x 2

3. (-4m

2 - 6m) - (6m + 4m 2

4. 27x

2 - 5y 2 + 12y 2 - 14x 2 5. 1 4 x 2 3 8 xy + 1 2 y 2 1 2 xy + 1 4 y 2 3 8 x 2

6. 24p

3 - 15p 2 + 3p - 15p 3 + 13p 2 - 7p

Example 1

Example 2

Exercises

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