Transcript Operations with Polynomials - Ellen Moore`s 7010 Portfolio

By: Ellen Moore
[email protected]
Adding
Subtracting
How to
How to
Examples
Examples
Practice
Practice
Multiplying a Binomial by a Binomial
How to
Examples
Practice
Standards
References
Adding Polynomials
You will combine like terms.
Remember like terms have exactly the
same variable, variables, and exponents.
To add them you will add or subtract the
coefficients. Whatever the signs say to do.
Remember the coefficients are the big
numbers.
Examples of adding
1.( 3x2 -4x + 8) + (2x - 7x2 – 5)
=(3x2 – 7x2) + (-4x +2x) + (8-5)
= - 4x2 – 2x + 3
2.(3n2 – 8 +2n) + ( 5n + 13 + n2)
= ( 3n2 + 1n2) + ( 2n + 5n) + (-8 +13)
=4n2 + 7n + 5
Practice on Adding
(2b3 -4b +b2) + ( -9b2 + 3b3 )
a. 11b3 -10b2 + 4b
b. 5b3 + 10b2 -4b
c. 5b3 -8b2 -4b
.
Wrong! Try again.
Wrong! Try again.
Subtracting Polynomials
Remember subtraction means to add the
opposite.
To subtract polynomials you will add the
opposite.
To add the opposite you will change the
signs of every term in the second
polynomial and then add.
Examples of Subtracting
1.(3n2 + 13n3 + 5n) – (7n + 4n3 )
= (3n2 + 13n3 +5n) + (-7n – 4n3 )
= ( 13n3 -4n3 ) + (3n2 ) + (5n-7n)
= 9n3 +3n2 -2n
2. ( 6y2 + 8y4 -5y)-( 9y4 -7y +2y2 )
= (6y2 +8y4 -5y) + (-9y4 +7y – 2y2 )
= (8y4 -9y4 ) + (6y2 -2y2 ) + (-5y +7y)
= -y4 + 4y2 + 2y
Practice on Subtracting
( -4y2 –y + 10) – ( 4y2 + 3y + 7)
a. 8y2 + 2y + 17
b.-8y2 + 2y +3
c. -8y2 -4y+3
That’s correct!
Multiplying two Binomials
To multiply two binomials you use the FOIL method.
F- Multiply the first term in each binomial.
O- Multiply the outside terms- first one in the first
binomial and last one in the second.
I- Multiply the inside terms which will be the last one in
the first binomial and the first in the second one.
L-Multiply the last term in each binomial.
Then you will combine like terms if you have any.
Usually the outsides and the insides yield like terms.
Examples of multiplying two binomials
( n+ 3) (n + 5) =
Firsts (n x n)=n2
Outsides (n x 5)=5n
Insides (3 x n)=3n
Lasts (3 x 5) = 15
n2 + 5n + 3n + 15 – collect like terms
= n2 + 8n + 15
Practice on Multiplying Two Binomials
1.( n + 6 ) ( n+ 2 )=
a. n2+ 6n + 2n + 8
b. n2 + 8n + 12
c. 2n2 + 8n +12
You got the correct answer.
Standards:
South Carolina State Standards
EA-2.7 Carry out a procedure ( including
addition, subtraction, multiplication, and
division by a monomial) to simplify
polynomial expressions.
References:
Glencoe Mathematics Algebra 1. Glencoe
McGraw-Hill.