Factoring algebraic expressions is one of the most important techniques you'll practice. Not much else can be done in terms of solving equations, graphing functions and conics, and working on applications if you can't pull out a common factor and simplify an expression. Factoring changes an expression of two or more terms into one big product, which is really just one term. Having everything multiplied together allows for finding common factors in two or more expressions and reducing fractions. It also allows for the application of the multiplication property of zero. Factoring is crucial, essential, and basic to algebra.
In this chapter, you work through factoring basics in the following ways:
Here are a few things to keep in mind as you factor your way through this chapter:
416–421 Use divisibility rules for numbers 2 through 11 to determine values that evenly divide the given number.
416. 88
417. 1,010
418. 3,492
419. 4,257
420. 1,940
421. 3,003
422–429 Write the prime factorization of each number.
422. 28
423. 45
424. 150
425. 108
426. 512
427. 500
428. 1,936
429. 2,700
430–443 Factor each using the GCF.
430. 24x4 − 30y8
431. 44z5 + 60a − 8
432. 300abc + 420xyz
433. 121x4 − 165z
434. 24x2y3 − 48x3y2
435. 36a3b − 24a2b2 − 40ab3
436. 9z−4 + 15z−3 − 27z−1
437. 20y3/4 − 25y1/4
438. 16a1/2b3/4c4/5 − 48a3/2b7/4c9/5
439. 8x2(5x − 1) + 6x3(5x − 1)
440. 36x−3y4 + 20x−5y2
441. 125x−3y−4 + 500x−5y−2
442. x(3x − 1)2 + 2x2(3x − 1)
443. 4x3(x − 4)4 − 6x4(x − 4)3
444–455 Reduce the fractions by dividing with the GCF of the numerator and denominator.
444.
445.
446.
447.
448.
449.
450.
451.
452.
453.
454.
455.