Overhead Sheets
A.4A
Simplifying,
Transforming,
Solving
1
Monomials
A monomial is an
expression that is a product
of numbers, variables, and
their degree.
Examples:
 x
 3x2y3z
 -22m4
2
Polynomials
A polynomial is a monomial
or a sum of monomials.
Some polynomials have
specials names.
A binomial is the sum of
two monomials:
 7xyz + y2z
x + 1
 2x – 3yz
3
A trinomial is the sum of
three monomials.
 4a2 + 5a + 9
 12m3n2 – 8 mn2 + 3
If a polynomial contains
more then 3 terms, we just
call it a polynomial.
4
The degree of a monomial is the sum of
the exponents of all its variables.
Monomial Degree
6x4
5y
8
4
1
0
The degree of a polynomial is the greatest
degree of any term in the polynomial.
Degree of
each term
4
Degree of
Polynomial
-5x2y2 + 2x2 +7 -5x2y2, 2x2, 7
4, 2, 0
4
2x + y – 2x2y + 4 2x, y, 2x2y, 4
1, 1, 3, 0
3
Polynomial
Terms
6xy3
6xy3
4
5
On TAKS, you will be asked to simplify
polynomial expressions, for example:
Which of the following expressions is
equivalent to 4(n – 3)(n +2)?
A
B
C
D
4n2 – 4n – 24
4n2 + 4n + 24
4n2 – 24
4n2 + 4n – 24
Remember: To multiply 2 binomial, we
use “FOIL”
1st ∙ 1st
outside ∙ outside
inside ∙ inside
last ∙ last
6
Remember: when we have a problem like
this
6(x + 2)
We DISTRIBUTE!!
6 ∙ x + 6 ∙2 = 6x + 12
TAKS Examples:
Which expression is equivalent to the
following expression?
½ x(4x – 6) + 3(x2 – 1)
A
B
C
D
5x2 – 3x + 3
x2 + 3x – 6
5x2 – 3x – 3
-x2 + 3x + 3
7
Solve the equation 2a – 6 + 5a = 3a + 10
for a.
Which expression is equivalent to
(5n − 2)3n – (5n − 2) (n − 1)
A
B
C
D
n–1
3n2 – 3n
10n2 – 13n + 2
10n2 +n – 2
8
Which expression is equivalent to
2/3 (3x – 15y) + (9y – 11x)
A
B
C
D
-9x – y
11x – 21y
10x – 4y
-9x – 26y
Simplify the algebraic expression
3(x + 3) – 2(x + 3)
F
G
H
J
x+3
x–3
-6x2 – 54
6x2 + 3
9
The area of a rectangle is given by the
equation 2l2 – 5l = 18, in which l is the
rectangle’s length. What is the length
of the rectangle?
F
G
H
J
1.5
2
4.5
6
In the equation y = 2x2 – 5x – 18,
which is a value of x when y = 0?
A
B
C
D
-18
1½
2
4½
10
Which equation best represents the
area, A, of the rectangle below?
A
B
C
D
A = 2x + 2(x + c)
A = x2 + (x + c) 2
A = x(x + c)
A = 2x(x + c)
11