Multiplying and Dividing Polynomials by a Constant
Lesson 25
Ch 5.5
When multiplying a monomial by a polynomial we must multiply that
monomial by each term in the polynomial. This multiplication is called the
distributive law in which the monomial is ‘distributed’ (multiplied) to
each term.
6 (x + 8) =
Algebra Tiles:
Distributive Property:
4( -3x + 4) = 4(-3x) + 4(4)
4( -3x + 4)
-x
-x
-x
1111
= -12x + 16
1
1
1
4 rows of –x tiles and four 1tiles
There are twelve –x tiles and
sixteen 1-tiles.
So 4( -3x + 4) = -12x + 16
1. Expand using distributive law
3(x – 1)
2. Expand each of the following using the distributive law.
a. 2(x +1)
b. − 4(2x −1)
c. 3(3x − 2y +1)
When you have more than one term divided by the same term you must
divide EACH term by the denominator on the bottom.
Algebra Tiles
Write the Quotient as the sum of 2
fractions
ସ௫ మ ି଼
ସ
2
Arrange four x tiles and eight -1 tiles
into 4 equal rows.
ସ௫ మ ି଼
ସ
=
ସ௫ మ
ସ
+
= x2 – 2
In each row there is one x2 tile and
ସ௫ మ ି଼
two -1 tiles, so
= x2 - 2
ସ
ି଼
ସ
Dividing Polynomials
When you have more than one term divided by the same term you must
divide EACH term by the denominator on the bottom.
a.
ଶ଴௫ ା ହ
ହ
b.
ସଶ௬ మ ି ହ଺
ିଵସ
c.
ି଼௫ ା ଶସ௫ା଻ଶ
଼
(Worksheet 25)