Overhead Sheets

A.4A

Simplifying,

Transforming,

Solving

Monomials

A monomial is an expression that is a product of numbers, variables, and their degree.

Examples:

· x

· 3x2y3z

· -22m4

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

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.

The degree of a monomial is the sum of the exponents of all its variables.

Monomial / Degree
6x4 / 4
5y / 1
8 / 0

The degree of a polynomial is the greatest degree of any term in the polynomial.

Polynomial / Terms / Degree of each term / Degree of Polynomial
6xy3 / 6xy3 / 4 / 4
-5x2y2 + 2x2 +7 / -5x2y2, 2x2, 7 / 4, 2, 0 / 4
2x + y – 2x2y + 4 / 2x, y, 2x2y, 4 / 1, 1, 3, 0 / 3

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 4n2 – 4n – 24

B 4n2 + 4n + 24

C 4n2 – 24

D 4n2 + 4n – 24

Remember: To multiply 2 binomial, we use “FOIL”

1st ∙ 1st

outside ∙ outside

inside ∙ inside

last ∙ last

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 5x2 – 3x + 3

B x2 + 3x – 6

C 5x2 – 3x – 3

D -x2 + 3x + 3

Solve the equation 2a – 6 + 5a = 3a + 10 for a.

Which expression is equivalent to

(5n − 2)3n – (5n − 2) (n − 1)

A n – 1

B 3n2 – 3n

C 10n2 – 13n + 2

D 10n2 +n – 2

Which expression is equivalent to

2/3 (3x – 15y) + (9y – 11x)

A -9x – y

B 11x – 21y

C 10x – 4y

D -9x – 26y

Simplify the algebraic expression

3(x + 3) – 2(x + 3)

F x + 3

G x – 3

H -6x2 – 54

J 6x2 + 3

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 1.5

G 2

H 4.5

J 6

In the equation y = 2x2 – 5x – 18, which is a value of x when y = 0?

A -18

B 1½

C 2

D 4½

Which equation best represents the area, A, of the rectangle below?

A A = 2x + 2(x + c)

B A = x2 + (x + c) 2

C A = x(x + c)

D A = 2x(x + c)

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