Algebra 1 Common Core Student Edition, Grade 8-9

How do you get

started?

Divide the first term in

the dividend by the first

term in the divisor. Here,

you divide 3d 2 by d.

Think
Why add a term w ith
a coefficient o f 0?
If the dividend is missing a
term when w ritten in
standard form, you must
add the term w ith a
coefficient of 0 to act as
a placeholder.

The process of dividing a polynom ial by a binom ial is sim ilar to long division of real

num bers. You write th e answ er as q u o tien t + remamderdivisor

Problem 2 Dividing by a Binomial

What is (3d 2 - 4 d + 13) + (d + 3)?

Step 1 Begin th e long division process. Align terms by their degrees. Put 3d

above - 4 d o f t h e dividend. , „.

d + 3)3d 2 — 4d + 13 Divide: 3d2 + d = 3d.

3d2 + 9d Multiply: 3d(d+3) = 3d2 + 9d. Then subtract.

— 1 3 d + 1 3 Bring dow n 13.

Step 2 R epeat the process: divide, m ultiply, subtract, a n d b ring down.

3d - 13

d + 3)3d2 - 4d + 13

3d2 + 9 d

Align terms by their degrees. Put

• 1 3 above 13 of the dividend.

— 1 3 d + 1 3 Divide: -13d 4- d = -13.

• 1 3 d - 39 Multiply: — 13 ( d + 3) = - 1 3 d - 39. Then subtract.
  5 2 The remainder is 52.

The answ er is 3d - 13 +a + 3

G o t It? 2. What is (2m2 — m — 3) 4- (m + 1)?

W hen th e dividend has a m issing term , ad d th e m issing term w ith a coefficient of zero.

Dividing Polynomials W ith a Zero Coefficient

Geometry The width w of a rectangle is 3z — 1. The area A of the rectangle is

1 8 z 3 — 8 z + 2. What is an expression for the length of the rectangle?

Area: 18z3- 8 z + 2

Width: 3 z -1

The length of the

rectangle

. Mm
Use the formula for the area of a rectangle,
A = ( w. Divide A by w to solve for i.

6z + 2z - 2

3z — 1)18z3 + 0z2-8z + 2

18z3 — 6z2

6z2 - 8z

6z2 - 2z

— 6 z+ 2

—6 z + 2

0

An expression for th e length of th e rectangle is 6z2 + 2z — 2.

The dividend has no z 2 -term. So rewrite

the dividend to include a z 2-term with

coefficient 0.

[ PowerAlgebra.com ^! |[Lesson 11-3 D ividing Polynom ials 6 7 9