additional exercises 5.1 i - cabrillo college - …hpayne/math 152/additional exercises...name _____...
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Name __________________________________ Date _________________________
AE-156
Additional Exercises 5.1 Form I
Introduction to Polynomials and Polynomial Functions
Complete the following by naming (a) each term of the given polynomial, (b) the coefficient of each term, (c) the degree of each term and finally, (d) the degree of the polynomial. 1. xx 34 2 ! a. terms 1a. _______________ b . coefficient of each term b. _______________ c. degree of each term c. _______________ d. degree of polynomial d. _______________ 2. xxx 546 23 !+ a. terms 2a. _______________ b . coefficient of each term b. _______________ c. degree of each term c. _______________ d. degree of polynomial d. _______________ 3. 643 23 !+! xxx a. terms 3a. _______________ b . coefficient of each term b. _______________ c. degree of each term c. _______________ d. degree of polynomial d. _______________ For exercises 4 – 6, (a) determine the leading coefficient of the polynomial and (b) the degree of the polynomial. 4. 425 538 yyxx +! 4a. _______________ b. _______________
Name __________________________________ Date _________________________
AE-157
5. 624526 5829 yyxyxyx !++ 5a. _______________ b. _______________ 6. 5452637 1921210 yxyxyxyx !++ 6a. _______________ b. _______________ 7. Given the function 12)( 2 ++= xxxf , find f (–2). 7. _______________ 8. Given the function 53)( 3 !!= xxxg , find f (–1). 8. _______________ Determine whether the graph shown is the graph of a polynomial function. 9. 9. _______________ 10. 10. _______________ For exercises 11 – 13, use the Leading Coefficient Test to determine the end behavior of the graph of each function. 11. 4)( 2 += xxf 11. _______________
Name __________________________________ Date _________________________
AE-158
12. 32)( 3 ++!= xxxg 12. _______________ 13. 12)( 2 !!!= xxxh 13. _______________ Add the polynomials. 14. )223()862( 22 +!+++ xxxx 14. _______________ 15. )432()55( 33 !+++! xxxx 15. _______________ 16. )347()882( 4646 xxxxxx ++++! 16. _______________ Subtract the polynomials. 17. )52()734( 22 ++!++ xxxx 17. _______________ 18. )1073()856( 22 !!!+! xxxx 18. _______________ 19. )1052()5633( 23234 !!!+!+ xxxxx 19. _______________ 20. )343()725( 2222 yxyxyxyx !+!+! 20. _______________
Name __________________________________ Date _________________________
AE-165
Additional Exercises 5.2 Form I
Multiplication of Polynomials
Multiply the monomials. 1. )3)(6( 32 xx 1. _______________ 2. )4)(2( 42 xx! 2. _______________ 3. )6)(5( 5422 yxyx 3. _______________ 4. )4)(8( 243 xyyx !! 4. _______________ Use the distributive property to multiply. 5. )53(4 32 !xx 5. _______________ 6. )842(5 2 !+! xxx 6. _______________ 7. )65(2 22 yxxyxy + 7. _______________ 8. )4123(3 462 ababab +! 8. _______________ Find each product using either a horizontal or a vertical format. 9. )63)(2( 2 +++ xxx 9. _______________ 10. )152)(5( 2 +!! xxx 10. _______________
Name __________________________________ Date _________________________
AE-166
11. )1)(1( 2 !!+ xxx 11. _______________ 12. )43)(9( 2 !+! aaa 12. _______________ Multiply. 13. )8)(6( ++ xx 13. _______________ 14. )3)(7( !! xx 14. _______________ 15. )9)(9( !+ yy 15. _______________ 16. )23)(32( !+ xx 16. _______________ 17. 2)5( !a 17. _______________ 18. 2)11( +y 18. _______________ 19. )125)(72( baba !+ 19. _______________ 20. 2)5( yx + 20. _______________
Name __________________________________ Date _________________________
AE-171
Additional Exercises 5.3 Form I
Greatest Common Factors and Factoring By Grouping
Factor the greatest common factor from each polynomial. 1. xx 303 2 ! 1. _______________ 2. xxx 251015 23 +! 2. _______________ 3. 47 3yy ! 3. _______________ 4. 24332 271836 bababa +! 4. _______________ Factor out the negative of the greatest common factor. 5. 147 +! x 5. _______________ 6. yx 369 2 +! 6. _______________ 7. 572 !+! xx 7. _______________ Factor the greatest common binomial factor from each polynomial. 8. )10(2)10( +!+ yyx 8. _______________ 9. )12(5)12(4 +!+ yyx 9. _______________ 10. )8()8(2 !!! xxy 10. _______________
Name __________________________________ Date _________________________
AE-172
Factor by grouping. 11. 48862 +++ yyy 11. _______________ 12. 4267 !+! baab 12. _______________ 13. 1052 +++ yxxy 13. ______________ 14. 88 +++ yxxy 14. _______________ 15. yxxyx 442 !+! 15. _______________ 16. 22 96128 yxyxyx !+! 16. _______________ 17. abbyayy !+!2 17. _______________ 18. babaa 4386 2 !!+ 18. _______________ 19. yxyxx 1640615 2 !!+ 19. _______________ 20. yxyxx 10252 !+! 20. _______________
Name __________________________________ Date _________________________
AE-177
Additional Exercises 5.4 Form I
Factoring Trinomials
Factor each polynomial completely, or state that the polynomial is prime. 1. 342 ++ xx 1. _______________ 2. 1272 ++ xx 2. _______________ 3. 862 +! xx 3. _______________ 4. 462 +! xx 4. _______________ 5. 1832 !+ yy 5. _______________ 6. 672 ++ aa 6. _______________ 7. 4062 !! xx 7. _______________ 8. 24273 2 ++ xx 8. _______________ 9. 202 !+ xx 9. _______________ 10. 12102 2 +! yy 10. _______________
Name __________________________________ Date _________________________
AE-178
11. 132 2 ++ xx 11. _______________ 12. 443 2 !+ xx 12. _______________ 13. 584 2 !+ xx 13. _______________ 14. 1253 2 !! xx 14. _______________ 15. 5412 2 !! xx 15. _______________ 16. 122512 2 +! xx 16. _______________ 17. 22 232 baba !! 17. _______________ 18. 1248 2 !+ xx 18. _______________ 19. xxx 451212 23 !+ 19. _______________ 20. 22 103 baba !! 20. _______________
Name __________________________________ Date _________________________
AE-183
Additional Exercises 5.5 Form I
Factoring Special Forms
Factor each difference of two squares. 1. 362 !x 1. _______________ 2. 812 !y 2. _______________ 3. 925 2 !a 3. _______________ 4. 22 2516 yx ! 4. _______________ 5. 12 !x 5. _______________ 6. 1214 2 !y 6. _______________ Factor each perfect square trinomial. 7. 64162 ++ xx 7. _______________ 8. 100202 +! xa 8. _______________ 9. 962 ++ yy 9. _______________ 10. 9124 2 ++ xx 10. _______________
Name __________________________________ Date _________________________
AE-184
11. 22 168 yxyx +! 11. ______________ 12. 22 254016 baba +! 12. _______________ Factor each polynomial using the formula for the sum or difference of two cubes. 13. 273 +x 13. _______________ 14. 643 !y 14. _______________ 15. 88 3 +x 15. _______________ 16. 827 3 +y 16. _______________ 17. 33 ba ! 17. _______________ 18. 1253 +x 18. _______________ Factor each polynomial completely, or state that the polynomial is prime. 19. 24 164 xx ! 19. _______________ 20. 50202 2 ++ aa 20. _______________
Name __________________________________ Date _________________________
AE-189
Additional Exercises 5.6 Form I
A General Factoring Strategy
Factor completely or state that the polynomial is prime. 1. 1032 !+ xx 1. _______________ 2. 169 2 ++ yy 2. _______________ 3. xx !2 3. _______________ 4. 254 2 !x 4. _______________ 5. 33 ba ! 5. _______________ 6. 18112 +! aa 6. _______________ 7. 2212 yxyx !! 7. _______________ 8. 132 ++ xx 8. _______________ 9. 753 2 !y 9. _______________ 10. 782 +! yy 10. _______________
Name __________________________________ Date _________________________
AE-190
11. 1099 2 !! xx 11. _______________ 12. 812 !x 12. _______________ 13. 22 24132 yxyx !+ 13. _______________ 14. 42 +x 14. _______________ 15. 1025 !+! yxxy 15. _______________ 16. 200300100 2 +! aa 16. _______________ 17. 242 2 +! xx 17. _______________ 18. 49 2 !x 18. _______________ 19. bbxxx 442 +++ 19. _______________ 20. 827 3 +x 20. _______________
Name __________________________________ Date _________________________
AE-195
Additional Exercises 5.7 Form I
Polynomial Equations and Their Applications
Use factoring to solve each polynomial equation. 1. 0862 =+! xx 1. _______________ 2. 0542 =!! xx 2. _______________ 3. 2452 =! xx 3. _______________ 4. xx 7182 =! 4. _______________ 5. 0276 2 =+ xx 5. _______________ 6. 0)4( =+xx 6. _______________ 7. 050355 2 =+! xx 7. _______________ 8. 0492 =!x 8. _______________ 9. xx 79 2 = 9. _______________ 10. xxx 1223 =+ 10. _______________
Name __________________________________ Date _________________________
AE-196
11. 02 =! xx 11. _______________ 12. 0100202 =+! xx 12. _______________ 13. 1522 =+ xx 13. _______________ 14. yyy 32025 23 ++ 14. _______________ 15. 33)1)(9( =++ xx 15. _______________ 16. 0123 24 =! xx 16. _______________ 17. 11)7)(3( =!+ xx 17. _______________ 18. 273 2 =x 18. _______________ Solve the problem. Use only one variable. 19. The length of a rectangle storage room is 9 feet longer 19. _______________ than its width. If the area of the room is 162 square feet, find the dimensions of the room. 20. An object is thrown upward from the top of a 160 foot 20. _______________ building with an initial velocity of 48 feet per second. The height h of the object after t seconds is given by the quadratic equation .1604816 2 ++!= tth When will the object hit the ground?
