Homework Practice
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1 2 3 4
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Algebra
1 2 3 4
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Factoring Polynomials of Degree 3
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Factoring Polynomials of Degree 3 Factoring a 3 - b 3 An expression of the form a 3 - b 3 is called a difference of cubes. The factored form of a 3 - b 3 is (a - b)(a 2 + ab + b 2) : (a - b)(a 2 + ab + b 2) = a 3 - a 2 b + a 2 b - ab 2 + ab 2 - b 3 = a 3 - b 3 For example, the factored form of 27x 3 - 8 ( a = 3x, b = 2 ) is (3x - 2)(9x 2 + 6x + 4) . Similarly, the factored form of 125x 3 -27y 3 ( a = 5x, b = 3y ) is (5x - 3y)(25x 2 +15xy + 9y 2) . To factor a difference of cubes, find a and b and plug them into (a - b)(a 2 + ab + b 2) . Factoring a 3 + b 3 An expression of the form a 3 + b 3 is called a sum of cubes. The factored form of a 3 + b 3 is (a + b)(a 2 - ab + b 2) : (a + b)(a 2 - ab + b 2) = a 3 + a 2 b - a 2 b - ab 2 + ab 2 + b 3 = a 3 - b 3 .
Words for Operations
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Handout Module 2 Review ? Words for Operations Subtraction Minus Difference between From Less Less than Fewer than Decreased by Take away ?a number minus 2? ?the difference between a number? ?2 from a number? ?a number less 3? ?2 less than a number? ?2 fewer than a number? ?a number decreased by 2? ?a number take away 2? x ? 2 x ? 8 n ? 2 n ? 3 y ? 3 y ? 2 x ? 2 x ? 2 Addition Plus And Added to Greater than More than Increased by Total Sum of ?a number plus 2? ?3 and a number? ?8 added to a number? ?3 greater than a number? ?3 more than a number? ?a number increased by 2? ?the total length? ?the sum of the length and width? x + 2 3 + n x + 8 n + 3 y + 3 y + 2 l1 + 12 + ? l + w Multiplication Times Product At double, triple, etc. Twice Of (fractions of)
Algebra Help
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Applying the Fundamental Concepts of Algebra An understanding of the fundamental concepts of algebra and of how those fundamental concepts may be applied is necessary in many professional and most technical careers. For engineers and scientists it is an essential requirement. The fundamental concepts of algebra are described in the preceding section of this article. How these concepts may be applied to aid in the solution of various types of mathematical problems is explained here. USING REAL NUMBERS
Uniform accelerated motion vocab
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Speed: The time rate of motion Slope = change in distance/change in time (rise/run) Scalar: the distance moved per unit of time Average speed (scalar): the ratio of the total distance traveled to the total time Total distance/elapsed time (m/s) Instantaneous speed (scalar): the speed of an object at a particular moment in time The slope of the line that is tangent to the curve at a given point Velocity (vector): speed in a particular direction Average velocity (vector): the total displacement divided by the total elapsed time Displacement /Elapsed time = (?x)/ (?t) Instantaneous velocity: The speed and direction an object moves at a particular moment in time
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