Math 114-Review Final Exam Factor completely. If a polynomial cannot be factored, say it is prime. 1) 5x4 + 8x6
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2) 4t5 - 4t4 - 24t3
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3) x3 - 9x + 2x2 - 18
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Solve the equation by factoring. 4) x2 - 16 = 15x
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Solve the problem. 5) The side of a square equals the length of a rectangle. The width of the rectangle is 4 meters longer than its length. The sum of the areas of the square and the rectangle is 160 square centimeters. Find the side of the square. Find the value(s) of the variable for which the rational expression is undefined. x2 - 81 6) x2 + 14x + 48
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Simplify the rational expression. Assume that no variable has a value which results in a denominator with a value of zero. y2 + 10y + 24 7) 7) y2 + 13y + 36 Perform the indicated operation. 2x + 6y x + 3y 8) · 2 2 3 x + 6xy + 9y
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x2 - 3x x + 4 ÷ x2 - 9 x2 + 7x + 12
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42x - 120 240 - 22x + 4x + 24 4x + 24
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8x + 10 3x + 9 - x - 9 x - 9
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21x2 15x + 7x - 5 5 - 7x
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9 9 - x + 8 5x + 40
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1
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15 x + 2x - 8 x2 - 16
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Simplify the complex rational expression. 1 1 - 25 x2 15) 1 1 + 5 x
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Solve the rational equation. Check for extraneous solutions. 1 90 16) 1 + = x x2
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5 3 3x + 15 + = x + 15 x - 7 x2 + 8x - 105
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Add or subtract, as indicated. Assume that all variables represent positive real numbers. 18) 3 27 - 8 192 - 3 108 19) x 2x + 6 18x3 + 5x 18x
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Find the product and simplify. Assume all variables represent nonnegative real numbers. 20) ( 13 + 3)( 13 - 3) 21) (2 x - 7)2
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Rationalize the denominator of the expression. Assume that all variables represent positive real numbers. 35 22) 22) 7x
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64 5
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10 26 + 5
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Solve the equation. 25) 4x + 1 + 3 = 10
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22x - 55 = x + 3
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x - 3 = x - 21
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Solve the quadratic equation using completing the square. 28) x2 = 8x + 16
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Solve the equation using the quadratic formula. 29) 4x2 + 8x + 1 = 0
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Solve the problem. 30) The area of a rectangular wall in a classroom is 133 square feet. Its length is 2 feet shorter than three times its width. Find the length and width of the wall of the classroom. 31) A model rocket is launched from the ground with an initial speed of 40 feet per second. The equation that models its height, h feet, off the ground t seconds after it was fired is h = - 16t2 + 40t
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(a) How high is the rocket 1.5 seconds after it was fired? (b) How long will it take the rocket to return to the earth? Graph the quadratic equation by filling in the table and plotting the points. 32) y = x2 - 4x + 3 x y -1 0 1 2 3 4 5
The equation that models its height, h feet, off the ground t seconds after it was fired is h = - 16t2 + 40t. (a) How high is the rocket 1.5 seconds after it was fired?
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