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Chapter 8

Dividing Algebraic Expressions

Division is the opposite or inverse of multiplication. Instead of adding exponents, you subtract the exponents of like variables. When dividing an expression containing several terms by an expression containing just one term, you have two possible situations: the divisor evenly divides each term, meaning fractions formed from each term and the divisor reduce to denominators of 1, or the divisor doesn’t evenly divide one or more of the terms. What you do with the second situation depends on the application you’re working on at the time. The problems in this chapter present various options.

The Problems You’ll Work On

The problems in this chapter are all about division and include the following:

 Dividing several terms by a number

 Dividing several terms by a term containing numerical and variable factors

 Dividing several terms by a binomial, using long division

 Dividing several terms by a binomial, using synthetic division

 Dividing by trinomials

What to Watch Out For

As you work through dividing one expression after another, watch out for the following:

 Assigning the correct sign to each term in the result

 Remembering to change the sign of each term when dividing by a negative term

 Changing the signs of all products of quotient term times divisor term in each step of a long division problem

 Inserting zeros for missing terms when using synthetic division

 Changing the sign of the number in the binomial when setting up a synthetic division problem

 Starting with an exponent one smaller than that in the divisor when writing the quotient in a synthetic division problem

Dividing with Monomial Divisors

366–375 Divide each numerator by the monomial.

366.

367.

368.

369.

370.

371.

372.

373.

374.

375.

Monomial Divisors and Remainders

376–385 Divide each numerator by the monomial. Write any remainders as fractions.

376.

377.

378.

379.

380.

381.

382.

383.

384.

385.

Using Long Division to Divide with Binomials

386–395 Divide each numerator by the binomial, using long division. Write any remainders as fractions.

386.

387.

388.

389.

390.

391.

392.

393.

394.

395.

Dividing with Binomials Using Synthetic Division

396–405 Divide each numerator by the binomial, using synthetic division. Write any remainders as fractions.

396.

397.

398.

399.

400.

401.

402.

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.