Transcript 2.1&2.2

2.1 Sums and Differences
of Polynomials
Goals
 SWBAT simplify expressions for sums
and differences of polynomials
 SWBAT solve first-degree equations in
one variable
Definitions
monomial
A
is a numeral, a
variable, or an indicated product of a
numeral and one or more variables.
 Example: 2, m , 4ab, 9 x y
2
3
2
Definitions
n
ax
 When looking at the monomial
, the
number denoted by a is called the
coefficient
of the variable.
n
 The symbol x represents a power
of x, where x is called the base
exponent
and n is called the
.
Definitions
 A monomial with no variable (i.e. 9 or -6) is
called a
.
constant
degree
 The
of a monomial is
the exponent, n. If the monomial contains
more than one variable, the degree of the
monomial is the sum
of the exponents.
 Example: What is the degree of 8a 2 b 4
What is the coefficient?
?
Definitions
 A monomial or sum of monomials is called a
polynomial
.
 The monomials of the expression are called
terms
the
of the polynomial. The
coefficients on each term of the polynomial are
called the coefficients of the polynomial.
degree
 The
of a polynomial is the
degree of the term with the highest degree.
State the coefficients and the degree
of each polynomial.
1.
5 x  9 x  6 x  22
7
3
5, -9, 6, -22
Degree: 7
2.
3a b  3a b  9ab
5
2
2
3, -3, -9
Degree: 6
Definitions
like
 Two monomials are said to be
terms
if they have the same
variable(s) with the same exponent(s) and their
only difference is their coefficient.
binomial
 A
is a polynomial with two
trinomial
terms. A
is a polynomial with
three terms.
3
Example:Binomial: 7 x  4 x
Trinomial: 9 x 3  2 x  17
 When simplifying a polynomial expression,
combine the like terms by adding or
subtracting their coefficients.
Simplify.
3.
4.
 4 x  6 x  5x  3
2
10m n  13mn  m n  1
2
2
Given the two polynomials:
2
2
B

x
 2x  1
A  4 x  3 x and

2
 

sum
of the polynomials
A  B  4 x  3x  x  2 x  1
 this is the

 
2

A  B  4 x  3x  x  2 x  1
 this is the
polynomials.
2
difference
2
of the
 To simplify these expressions you can
add the like terms. If it is a subtraction
problem, distribute the negative and then
combine the like terms.
Questions 5-8: Find the sum or
difference and write the answer in
simplest form.
Let
A  5x  7 x  9
3
2
B  2 x  x  8
2
C  x  x  12
3
2
5. A + B
6. B – C
7. C – A
8. A + C - B
Questions 9-10: Simplify.
9.
 3c
10.
2 3x  74  x  8x  2x  5
2
 

 7c  4d   c  5c  10d 
2
2.2 Solving
Equations
 To solve an equation we can
transform the equation into an
equivalent equation to get the solution.
Ways to Transform and
Solve an Equation:
1. Substituting for either side of the given
equation an expression equivalent to it.
2. Adding to or subtracting from each side
of the given equation.
3. Multiplying or dividing each side of the
equation by the same nonzero number.
*This also includes multiplying by a
reciprocal*
 Make sure when transforming equation to
only combine
terms!
like
Solve the equation.
1.
m
26
5
Solve the equation.
2.
4v  21  19  v
Solve the equation.
3.
5x  x  6  6
Your turn!
Solve #4-6
Solve the equation.
7.
512  32  y   2 y  21  y 
Solve the equation.
8.
3
5
2b  5  3b  9  6
4
4
Solve for the variable indicated.
9.
Solve for n.
1
5c  dn  3c
2
Solve for the variable indicated.
10. Solve for x
4kx  7h  kx