math 121 review. if i only knew ab sum a + b difference a-b product ab 47 -47 4-7 -4-7

Math 121Review

If I only knew…

a b SUMa + b

DIFFERENCEa-b

PRODUCTab

QUOTIENT B TO THE A POWER

4 7

-4 7

4 -7

-4 -7

Did you know???

• Did you know???????• You can never... actually reach the end of a rainbow, where a

pot of gold supposedly awaits. As you move, the rainbow that your eyes see moves as well, because the raindrops are at different spots in the atmosphere. The rainbow, then, will always "move away" at the same rate that you are moving.

Tobey & Slater, Beginning Algebra, 7e 5© 2010 Pearson Prentice Hall. All rights reserved.

Multiplying PolynomialsUse the distributive property to multiply a monomial by a polynomial.

Example:a.) Multiply. 3(c – 4)

3(c – 4) = 3(c) + 3(– 4)

= 3c – 12

b.) Multiply. 2x3(x2 – x + 2)

2x3(x2 – x + 2) = 2x3(x2) + 2x3(– x) + 2x3(2)

= 2x5 – 2x4 + 4x3


The FOIL MethodExample: Multiply using the FOIL method.

(7x + 3)(2x + 4)

= (7x)(2x)

(7x + 3)(2x + 4)

F

F

O

O+ (7x)(4) + (3)(2x)

I

I+ (3)(4)

L

L

= 14x 2 + 28x + 6x + 12= 14x 2 + 34x + 12


Scientific notation is the way that scientists easily handle very large numbers or very small numbers.


Scientific Notation

Scientific Notation A number is written in scientific notation if it is in the form a × 10n, where 1 a 10 and n is an integer.

8200 = 8.2 1000 = 8.2 103

Greater than 1 and less than 10

Power of 10

34,200,000 = 3.42 10000000 = 3.42 107

Scientific notation


Decimal Notation to Scientific Notation

Example: Write 67,300 in scientific notation.

67,300. = 6.73 10n

Starting position of decimal point

Ending position of decimal point

What power?

The decimal point was moved 4 places to the left, so we use a power of 4.

67,300 = 6.73 104

A number that is larger than 10 and written in scientific notation will always have a positive exponent as the power of 10.


Example: Write 0.048 in scientific notation.

0.048 = 4.8 10n

Starting position of decimal point

Ending position of decimal point

What power?

The decimal point was moved 2 places to the right, so we use a power of –2.

0.048 = 4.8 10–2

A number that is smaller than 1 and written in scientific notation will always have a negative exponent as the power of 10.

Decimal Notation to Scientific Notation


Scientific Notation to Decimal Notation

Example: Write 9.1 104 in decimal notation.

9.1 104 = 9.1000 104 = 91,000

Move the decimal point 4 places to the right.

Example: Write 6.72 10–3 in decimal notation.

6.72 10–3 = 6.72 10–3 = 0.00672

Move the decimal point 3 places to the left.

math 121 review. if i only knew ab sum a + b difference a-b product ab 47 -47 4-7 -4-7

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