Math 121 Review

If I only knew…

ab SUM a + b DIFFERENCE a-b PRODUCT ab

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, 7e5 © 2010 Pearson Prentice Hall. All rights reserved. Multiplying Polynomials Use 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. 2x 3 (x 2 – x + 2) 2x 3 (x 2 – x + 2) = 2x 3 (x 2 ) + 2x 3 (– x) + 2x 3 (2) = 2x 5 – 2x 4 + 4x 3

Tobey & Slater, Beginning Algebra, 7e6 © 2010 Pearson Prentice Hall. All rights reserved. The FOIL Method Example: 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 x + 6x + 12 = 14x x + 12

Tobey & Slater, Beginning Algebra, 7e7 © 2010 Pearson Prentice Hall. All rights reserved. Scientific notation is the way that scientists easily handle very large numbers or very small numbers.

Tobey & Slater, Beginning Algebra, 7e8 © 2010 Pearson Prentice Hall. All rights reserved. Scientific Notation A number is written in scientific notation if it is in the form a × 10 n, where 1  a  10 and n is an integer. Scientific Notation A number is written in scientific notation if it is in the form a × 10 n, where 1  a  10 and n is an integer = 8.2  1000 = 8.2  10 3 Greater than 1 and less than 10 Power of 10 34,200,000 = 3.42  = 3.42  10 7 Scientific notation

Tobey & Slater, Beginning Algebra, 7e9 © 2010 Pearson Prentice Hall. All rights reserved. Decimal Notation to Scientific Notation Example: Write 67,300 in scientific notation. 67,300. = 6.73  10 n 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  10 4 A number that is larger than 10 and written in scientific notation will always have a positive exponent as the power of 10.

Tobey & Slater, Beginning Algebra, 7e10 © 2010 Pearson Prentice Hall. All rights reserved. Example: Write in scientific notation = 4.8  10 n 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 – = 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

Tobey & Slater, Beginning Algebra, 7e11 © 2010 Pearson Prentice Hall. All rights reserved. Scientific Notation to Decimal Notation Example: Write 9.1  10 4 in decimal notation. 9.1  10 4 =  10 4 = 91,000 Move the decimal point 4 places to the right. Example: Write 6.72  10 –3 in decimal notation  10 –3 = 6.72  10 –3 = Move the decimal point 3 places to the left.