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.
445.
446.
447.
448.
449.
450.
451.
452.
453.
454.
455.
Chapter 10
Factoring Binomials
A binomial is an expression with two terms. The terms can be separated by addition or subtraction. You have four possibilities for factoring binomials: (1) factor out a greatest common factor, (2) factor as the difference of perfect squares, (3) factor as the difference of perfect cubes, and (4) factor as the sum of perfect cubes. If one of these methods doesn’t work, the binomial doesn’t factor when using real numbers.
The Problems You’ll Work On
The problems in this chapter focus on the following:
Factoring when the two terms are the difference
