Class
Name
Date
Reteaching
7-10
A few important rules are needed for
suocessful division of a polynomial. When
dividing by a monomial, a single term, remember to divide each polynomial term
by the monomial and reduce the fraction.
Prohlem
What is (8x3
-3f
+
L6x)
+2i?
Solve
(8t
:
-3i
+ t6x)+2f
Division equals multiplieation by the reciprocal.
(8r' - s* + rcx1'
" +2x"
2x^)-
Multiply by
8x3 3x2 l6x
:----l--
2x2 2x2
the reciproca I of 2x2.
Use the Distributive Property.
2xz
:4r'-3ro+8
2x
Subtract exponents when dividing powers
with the same base.
:4r-:+!
2x
Simplify.
Exercises
Divide.
1. (Zxz
3. (x'
-
-
9x + 18) + 2x
3x4
+
1ox3
-1*' -
6) +
3*
2.
(l6f -
4.
(sf -2s* -
64)
+
4x3
1) + 5x
When a polynomial (many terms) is divided by a binomial (2 terms), the
polynomial terms should be in order from highest to lowest exponent.
To make the polynomial-4 +2x - 16* + 3.f division ready, put it in the
correct order for division, from greatest exponent to lowest. The correct order
for -4 + 2x - 16l + 3t' to be division ready is 3; - l6i + 2x - 4.
For any gaps or missing exponents, the place is held with 0. For example,l +
becomes x2
t
0x
+
1, 0x being the placeholder for the x term.
Pearson Texas Algebra
I
Copyright @ by Pearson Education, lnc., or its affiliates. All Rights Reserved
1
Date
Class
Name
7-10
Reteach ih g
(contin ued)
Dividing a polynomial by a binomial is similar to long dMsion.
Froblem
What is (p'
-3p
+ ?) +(p -2)?
Solve
p-2
-3p +2
Write the problem as long division.
Ask how many times p goes into p2 (p times). The variables must
align by exponent, so the p goes above 3p since both match.
p-2
p-2 p' -3p +2
p'-2p
-lp +2
p -l'
p -2V 1p *2
p' -2p
Multiply p times (p
down 2.
-
2). Subtract the product p2 2 2p. Bring
(-l
times). Multiply
Determine how many times p goes into -1p
(-1) times (p - 2) to get -lp + 2. Subtract the product -1p * 2.
There is no remainder.
-lp +2
-lp +2
Sop
-
2 goes intopz
-3p +2exactly p
- l times withnoremainder.
Exercises
Divide.
5.(& +4d-12)+(d-2)
6.b?-4y+4)*(y-2)
7.(f=b+l)+(x-1)
s.(b'-b-20)+(D-s)
Pearcon Texas Algebra
I
Copyright @ by Pearson Education, lnc., or its afiiliates. Afl Rights Reserved.