Algebra 1 Common Core Student Edition, Grade 8-9

(Marvins-Underground-K-12) #1
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
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