401 3 125 a 402 3216 b answer 2 6 6 36 b bb 403 3 2

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401. 3 125 a 402. 3 216 b Answer: 2 6 6 36 b b b 403. 3 2 54 m 404. 3 81 3 m Answer: 2 3 3 3 9 3 1 x x x 6.4 General Strategy for Factoring Polynomials Recognize and Use the Appropriate Method to Factor a Polynomial Completely In the following exercises, factor completely. 405. 3 2 24 44 x x 406. 4 3 24 9 a a Answer: 3 3 8 3 a a 407. 2 2 16 56 49 n mn m 408. 2 6 25 9 a a Answer:  2 9 3 1 a a 409. 4 2 5 45 u u 410. 4 81 n Answer:  2 9 3 3 n n n
OpenStax 6.5 Polynomial Equations This file is copyright 2017, Rice University. All Rights Reserved. 411. 2 64 225 j 412. 2 5 5 60 x x Answer:  5 3 4 x x 413. 3 64 b 414. 3 125 m Answer: 2 ( 5)( 5 25) m m m 415. 2 2 2 2 5 5 b bc cb c 416. 5 2 2 48 243 x y xy Answer:  2 2 3 4 9 2 3 2 3 xy x x x 417. 2 5 15 90 q q 418. 5 2 3 4 4 u v u v Answer: 2 2 1 1 u u u u 419. 4 10 6250 m 420. 2 60 75 30 x y xy y Answer: Prime 421. 2 2 16 24 9 64 x xy y 6.5 Polynomial Equations Use the Zero Product Property In the following exercises, solve. 422.  3 7 0 a a Answer: 3 7 a a   423.  5 1 6 1 0 b b
OpenStax 6.5 Polynomial Equations This file is copyright 2017, Rice University. All Rights Reserved. 424. 6 12 – 5 0 m m Answer: 0, 5/12 m m 425. 2 (2 1) 0 x 426.  3 2 5 6 0 m m m Answer: 5 0 3 2 m m m   Solve Quadratic Equations by Factoring In the following exercises, solve. 427. 2 9 20 0 x x 428. 2 72 0 y y Answer: 8, 9 y y   429. 2 2 11 40 p p 430. 3 2 3 2 0 q q q Answer: 0, 1, 2 q q q     431. 2 144 25 0 m 432. 2 4 36 n Answer: 3, 3 n n   433.  6 – 3 8 x x 434.  3 2 4 12 x x x Answer: 3/ 2, 1 x x   435. 3 2 16 24 9 p p p 436. 3 2 2 2 12 y y y Answer: 0, 2, 3 y y y  
OpenStax 6.5 Polynomial Equations This file is copyright 2017, Rice University. All Rights Reserved. Solve Equations with Polynomial Functions In the following exercises, solve. 437. For the function,   2 11 20, f x x x (a) find when   8 f x   (b) Use this information to find two points that lie on the graph of the function. 438. For the function,   2 9 18 5, f x x x (a) find when   3 f x   (b) Use this information to find two points that lie on the graph of the function. Answer: (a) 2 3 x or 4 3 x (b) 2 , 3 3 4 , 3 3 In each function, find: (a) the zeros of the function (b) the x -intercepts of the graph of the function (c) the y -intercept of the graph of the function. 439.   2 64 49 f x x 440.   2 6 13 5 f x x x Answer: (a) 5 2 x or 1 3 x   (b) 5 , 0 , 2 1 , 0 3 (c) 0, 5 Solve Applications Modeled by Quadratic Equations In the following exercises, solve. 441. The product of two consecutive numbers is 399. Find the numbers. 442. The area of a rectangular shaped patio 432 square feet. The length of the patio is 6 feet more than its width. Find the length and width. Answer: The length is 24 ft and the width is 18 ft. 443. A ladder leans against the wall of a building. The length of the ladder is 9 feet longer than the distance of the bottom of the ladder from the building. The distance of the top of the ladder reaches up the side of the building is 7 feet longer than the distance of the bottom of the ladder from the building. Find the lengths of all three sides of the triangle formed by the ladder

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