Core Concepts - 1.cdn.edl.io52x + xx2 ++52 The degree of a polynomial is the greatest degree of its...

Copyright © Big Ideas Learning, LLC Algebra 1 All rights reserved. Student Journal

207

7.1 Notetaking with Vocabulary (continued)

Name _________________________________________________________ Date __________

Core Concepts Polynomials A polynomial is a monomial or a sum of monomials. Each monomial is called a term of the polynomial. A polynomial with two terms is a binomial. A polynomial with three terms is a trinomial.

Binomial Trinomial 5 2x + 2 5 2x x+ +

The degree of a polynomial is the greatest degree of its terms. A polynomial in one variable is in standard form when the exponents of the terms decrease from left to right. When you write a polynomial in standard form, the coefficient of the first term is the leading coefficient.

Notes:

Extra Practice In Exercises 1–8, find the degree of the monomial.

1. 6s− 2. w 3. 8 4. 2abc−

5. 27x y 6. 2 34r s t 7. 310mn 8. 23

2x3 + x2 − 5x + 12

leading coefficient

constant term

degree

Algebra 1 Copyright © Big Ideas Learning, LLC Student Journal All rights reserved. 208


Name _________________________________________________________ Date _________

In Exercises 9–12, write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial. Then classify the polynomial by the number of terms.

9. 23 5x x+ + 10. 5 y 11. 5 83 6x x+ 12. 2 42f f f− +

In Exercises 13–16, find the sum.

13. ( ) ( )4 9 6 14x x− + + − 14. ( ) ( )3 2 7 5a a− − + +

15. ( ) ( )2 23 5 6 4x x x x+ + + − + − 16. ( ) ( )2 3 2 33 3 2 7 2t t t t t+ − + + −

In Exercises 17–20, find the difference.

17. ( ) ( )4 3 6g g− − − 18. ( ) ( )5 2 7 6h h− − − +

19. ( ) ( )2 25 3 8x x x− − − − − − 20. ( ) ( )2 3 3 26 4 5 7 3k k k k k+ − − + −



Name _________________________________________________________ Date _________

Extra Practice In Exercises 1–6, use the Distributive Property to find the product.

1. ( )( )2 1x x− − 2. ( )( )3 2b b− + 3. ( )( )2 4g g+ +

4. ( )( )1 2 5a a− + 5. ( )( )3 4 1n n− + 6. ( )( )3 3 2r r+ +

In Exercises 7–12, use a table to find the product.

7. ( )( )3 2x x− − 8. ( )( )1 6y y+ − 9. ( )( )3 7q q+ +

10. ( )( )2 5 3w w− − 11. ( )( )6 2 3 2h h− − − 12. ( )( )3 4 3 4j j− + +


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Name _________________________________________________________ Date __________

In Exercises 13–18, use the FOIL Method to find the product.

13. ( )( )2 3x x+ − 14. ( )( )3 2z z+ + 15. ( )( )2 4h h− +

16. ( )( )2 1 2m m− + 17. ( )( )4 1 3 4n n− + 18. ( )( )1 1q q− − +

In Exercises 19–24, find the product.

19. ( )( )22 1x x x− + − 20. ( )( )22 3 3 5a a a− + − 21. ( )( )21 1h h h+ − −

22. ( )( )23 4 1d d d+ − + 23. ( )( )23 2 5 2 1n n n+ − + 24. ( )( )22 3 3 1p p p+ − −


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Name _________________________________________________________ Date __________

Extra Practice In Exercises 1–18, find the product.

1. ( )23a + 2. ( )22−b 3. ( )24+c

4. ( )22 1x− + 5. ( )23 2−x 6. ( )24 3p− −

7. ( )23 2+x y 8. ( )22 3−a b 9. ( )24 5c d− +

10. ( )( )3 3− +x x 11. ( )( )5 5+ −q q 12. ( )( )11 11− +t t



Name _________________________________________________________ Date _________

13. ( )( )5 1 5 1− +a a 14. 1 11 14 4

b b + −

15. 1 1 1 12 3 2 3

c c + −

16. ( )( )2 2m n m n− + − − 17. ( )( )3 2 3 2j k j k− − − + 18. 1 16 62 2

a b a b + − +

In Exercises 19–24, use special product patterns to find the product.

19. 18 22• 20. 49 51• 21. 3 219 205 5

•

22. ( )231 23. ( )220.7 24. ( )2109

25. Find k so that 2 12 9kx x− + is the square of a binomial.



Name _________________________________________________________ Date _________

Extra Practice In Exercises 1–12, solve the equation.

1. ( )5 0x x + = 2. ( )12 0a a − = 3. ( )5 2 0p p − =

4. ( )( )2 1 0c c− + = 5. ( )( )2 6 3 18 0b b− + = 6. ( )( )3 5 3 5 0s s− − + =

7. ( )23 0x − = 8. ( )( )3 7 5 6 0d d+ − = 9. ( )( )2 8 2 8 0t t+ − =

10. ( ) ( )24 1 0w w+ + = 11. ( )( )6 3 6 3 0g g g− + = 12. ( )( )( )234 8 2 3 0m m m− + − − =


223


Name _________________________________________________________ Date __________

In Exercises 13–18, factor the polynomial.

13. 26 3x x+ 14. 4 34 20y y− 15. 418 6u u−

16. 7 67 2z z+ 17. 324 8h h+ 18. 415 45f f−

In Exercises 19–24, solve the equation.

19. 26 0k k+ = 20. 235 49 0n n− = 21. 24 52 0z z+ =

22. 26 72x x= − 23. 222 11s s= 24. 27 21p p=

25. A boy kicks a ball in the air. The height y (in feet) above the ground of the ball is modeled by the equation 216 80 ,y x x= − + where x is the time (in seconds) since the ball was kicked. Find the roots of the equation when 0.y = Explain what the roots mean in this situation.


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Name _________________________________________________________ Date __________

Extra Practice In Exercises 1–12, factor the polynomial.

1. 2 8 7c c+ + 2. 2 16 64a a+ + 3. 2 11 18x x+ +

4. 2 6 8d d+ + 5. 2 11 10s s+ + 6. 2 10 9u u+ +

7. 2 3 54b b+ − 8. 2 2y y− − 9. 2 3 18u u+ −

10. 2 56z z− − 11. 2 2 24h h+ − 12. 2 3 40f f− −



Name _________________________________________________________ Date _________


13. 2 13 40 0g g− + = 14. 2 5 6 0k k− + = 15. 2 7 10 0w w− + =

16. 2 30x x− = 17. 2 3 2r r− = − 18. 2 7 8t t− =

19. The area of a right triangle is 16 square miles. One leg of the triangle is 4 miles longer than the other leg. Find the length of each leg.

20. You have two circular flower beds, as shown. The sum of the areas of the two flower beds is 136 square feet.π Find the radius of each bed.



Name _________________________________________________________ Date _________


1. 22 14 36c c− − 2. 24 8 140a a+ − 3. 23 6 24x x− −

4. 22 2 60d d− − 5. 25 55 50s s+ + 6. 23 30 27q q+ +

7. 212 37 28g g− + 8. 26 11 4k k− + 9. 29 9 2w w+ +

10. 212 5 2a a+ − 11. 215 14 8b b+ − 12. 25 12 9t t+ −


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Name _________________________________________________________ Date __________

13. 212 5 2b b− + + 14. 26 15x x− + + 15. 260 11 1g g− − +

16. 22 6d d− − + 17. 23 4 1r r− − − 18. 28 14 5x x− + −

19. The length of a rectangular shaped park is ( )3 5x + miles. The width is ( )2 8x + miles. The area of the park is 360 square miles. What are the dimensions of the park?

20. The sum of two numbers is 8. The sum of the squares of the two numbers is 34. What are the two numbers?


237


Name _________________________________________________________ Date __________


1. 2 49s − 2. 2 81t − 3. 216 x−

4. 24 25g − 5. 236 121h − 6. 281 49k−

In Exercises 7–12, use a special product pattern to evaluate the expression.

7. 2 257 53− 8. 2 238 32− 9. 2 268 64−

10. 2 245 40− 11. 2 279 71− 12. 2 286 84−



Name _________________________________________________________ Date _________

In Exercises 13–18, factor the polynomial.

13. 2 16 64x x+ + 14. 2 28 196p p+ + 15. 2 26 169r r− +

16. 2 18 81a a− + 17. 236 84 49c c+ + 18. 2100 20 1x x− +


19. 2 144 0x − = 20. 29 49y = 21. 2 14 49 0c c+ + =

22. 2 4 4 0d d− + = 23. 2 2 13 9n n+ = − 24. 26 9

5 25k k− + = −

25. The dimensions of a rectangular prism are ( )1x + feet by ( )2x + feet by 4 feet. The volume of the prism is ( )24 1x − cubic feet. What is the value of x?



Name _________________________________________________________ Date _________

Extra Practice In Exercises 1–8, factor the polynomial by grouping.

1. 3 24 4b b b− + − 2. ac ad bc bd+ + +

3. 2 2 2d c cd d+ + + 4. 3 25 6 5 6t t t+ + +

5. 3 28 64 8s s s+ − − 6. 3 212 2 30 5a a a+ − −

7. 3 24 12 5 15x x x− − + 8. 3 221 18 35 30h h h+ − −


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Name _________________________________________________________ Date __________

In Exercises 9–16, factor the polynomial completely.

9. 34 4c c− 10. 4 2100 25x x− 11. 22 3 2a a+ −

12. 29 3 14x x+ − 13. 220 22 12p p+ − 14. 212 20 48x x− −

15. 3 23 2 21 14s s s+ − − 16. 4 32 10 5t t t+ − −


17. 23 21 30 0x x− + = 18. 25 5 30 0y y− − = 19. 4 281 0c c− =

20. 3 29 9d d d+ = + 21. 248 3 0n n− = 22. 3 23 16 48x x x+ = +

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