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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.

445.

446.

447.

448.

449.

450.

451.

452.

453.

454.

455.