Download Multiplying Polynomials

Multiplying
Polynomials
Module VII, Lesson 3
Online Algebra
VHS@PWCS
Multiplying Polynomials
Recall that to multiply a polynomial by a
monomial, we used the distributive
property.
3x(2x2 – 7x + 8)
3x(2x2) – 3x(7x) + 3x(8)
6x3 – 21x2 + 24x
Multiplying Binomials
We apply the distributive property when multiplying
binomials using a method called FOIL.
FOIL stands for:
( x + 5 )( x + 7 )
First – Multiply the first terms
Outside – Multiply the outside terms
Inside – Multiply the inside terms
Last – Multiply the last terms
x(x)+ 7x + 5x+ 5(7)
x2 +12x + 35
Try these using FOIL
(2x + 9)(3x – 10)
(x – 8)(x + 7)
First
First
x(x) = x2
Outside
7x
Inside
-8x
Last
-8(7) = -56
Put it all together:
x2 + 7x + -8x + -56
x2 - x - 56
2x(3x) = 6x2
Outside
2x(-10) = -20x
Inside
9(3x) = 27x
Last
9(-10) = -56
Put it all together:
6x2 + -20x + 27x + -56
6x2 + 7x - 56
Multiplying Polynomials by
Polynomials
(3x2 – 2x + 3)(2x + 7)
Like with adding and subtracting
polynomials it is easier to multiply
setting these on top of each other.
3x 2  2 x  3
2x  7
21x  14 x  21
6 x3  4 x 2  6 x
In this manner we can multiply as we
have always done.
2
6x3 + 17x2 – 8x + 21
1.
2.
3.
Multiply everything in the first factor
by 7
Multiply everything in the first factor
by 2x, using a placeholder.
Add the products.
Try these on your own.
(x – 3)(2x2 + 3x + 3)
2x2 + 3x + 3
x–3
-6x2 – 9x – 9
2x3 + 3x2 + 3x
2x3 - 3x2 - 6x - 9
(2t2 – 6t + 3)(2t – 5)
2t2 – 6t + 3
2t – 5
-10t2 + 30t – 15
4t3 – 12t2 + 6t
4t3 – 22t2 + 36t - 15
Wrap up
 We use FOIL to multiply 2 binomials
 First
 Outside
 Inside
 Last
 We can set up multiplying polynomials
as we have always done and follow
those rules.