403.
404.
405.
Dividing with Higher Power Divisors
406–415 Divide each numerator by the denominator, using long division. Write any remainders as fractions.
406.
407.
408.
409.
410.
411.
412.
413.
414.
415.
Chapter 9
Factoring Basics
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.
The Problems You’ll Work On
In this chapter, you work through factoring basics in the following ways:
Determining what divides a number by using the rules of divisibility
Creating prime factorizations of numbers
Finding a numerical GCF (greatest common factor)
Factoring out a GCF containing numbers and variables
Reducing fractions with monomial divisors
Reducing fractions with polynomial divisors
What to Watch Out For
Here are a few things to keep in mind as you factor your way through this chapter:
Making sure you apply divisibility rules correctly
Writing a prime factorization with the correct exponents on the prime factors
Checking that the terms remaining after dividing out a GCF don’t still have a common factor
Reducing only factors, not terms
Writing fractional answers with correct grouping symbols to distinguish remaining factors
Finding Divisors Using Rules of Divisibility
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
Writing Prime Factorizations
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
Factoring Out a GCF
430–443 Factor each using the GCF.
430.
431.
432.
433.
434.
435.
436.
437.
438.
439.
440.
441.
442.
443.
Reducing Fractions with a Common GCF
444–455 Reduce the fractions by dividing with the GCF of the numerator and denominator.
444.