Secondary Math 3 Honors - Polynomial and Polynomial Functions Test Review

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1 Name: Class: Date: Secondary Math 3 Honors - Polynomial and Polynomial Functions Test Review 1 Write 3x 2 ( 2x 2 5x 3 ) in standard form State whether the function is even, odd, or neither Show your work Answer the questions using an algebraic method Check by graphing 8 f(x) = x x 1 answer: 2 The polynomial x 3 + 6x 2 55x 252 expresses the volume, in cubic inches, of a shipping box, and the width is (x + 4) in If the width of the box is 16 in, what are the other two dimensions? (Hint: The height is greater than the depth) 9 f(x) = x 3 + 2x 4 answer: Height: Depth: 3 State the number of possible real zeros and turning points of f(x) = x 6 + 4x 5 5x 4 Then determine all of the real zeros by factoring Number of possible real zero: 10 Is the function graphed below even, odd, or neither? Number of possible turning points: Real Zeros: Simplify the given expression 4 ( 3x 5) 2x 2 ˆ + 6x 3 5 8x 2 ˆ 14x x x 2 2 ˆ 6 8x 2 ˆ 2x x x 2 ˆ 7 Divide using method of your choice 2x 3 4x 2 + 4x 3 by x 4 answer: 11 True or False A polynomial can have negative exponents as powers of the variables 12 True or False When two polynomials are subtracted the result is sometimes another polynomial Find the real solutions of the equation by graphing Round to 3 decimal places if necessary 13 x 3 + 2x + 2 = 0 1

2 Name: What are the real or imaginary solutions of each polynomial equation? 14 2x 3 3x 2 16x + 24 = 0 Factor the polynomial completely 18 7x 2 17x x 4 13x 2 = x 3 40x x x = x 3 24x x 17 20x 2 11x 4 = 0 What is the degree of the polynomial that generates the given data? 21 x y a linear model c quadratic model b cubic model d none of these What are the relative maximum and minimum of the function? Use interval notation to describe where the function is increasing or decreasing State the domain and range 22 f(x) = 4x 3 + x 2 3x Minimum: Maximum: Increasing: Decreasing: Domain: Range: 23 Describe the end behavior of the graph of f(x) = x 2 (x + 10)( 2x + 4) using limits a As x, f(x) + As x +, f(x) - b As x, f(x) - As x +, f(x) - c As x, f(x) - As x +, f(x) + d As x, f(x) + As x +, f(x) + 2

3 Name: 24 Use the remainder theorem to find P( 4) for P(x) = x 4 + 8x 3 10x 2 + x Graph y = 10x 2 9 x 4 How many turning points are there? State the domain and range Divide using long division 25 8x x 5 + x 4 + 7x 3 18x 2 ˆ + 30x 21 ( 2x + 3) Given a polynomial and one of its factors, find the remaining factors of the polynomial Write the polynomial in factored form Don t forget the given factor 26 12x 3 100x x + 30; x 6 Turning points: Domain : Range: 27 4x 3 48x 2 49x + 588; x For the given graph, a describe the end behavior, b determine whether it represents an odd-degree or even-degree polynomial function, and c state the number of real zeros 28 The perimeter of a rectangle is 24a + 4b The length of rectangle is 9a 2b Find the measure of the width a b c 3

4 Name: 31 A manufacturer produces boxes for a calculator company The boxes have a volume of 240cm 3 The height of each box is 6cm less than the width The length is 1 cm less than twice the width Find the dimensions Divide using synthetic division 32 Divide 20x x by (x + 2) 35 Determine the sign of the leading coefficient and the least possible degree of the polynomial for the given graph 33 What is a cubic polynomial function in standard form with zeros 4, 1, and 5? 34 Determine the zeros and the end behavior of f(x) = x(x 1)(x 3) 2 Then sketch a graph of the function 36 For the following function, find the intervals where the function is increasing or decreasing f(x) = x 3 4x 2 + x Is x + 4 a factor of f(x) = x x x 7 Zeros: End behavior: 4

5 Secondary Math 3 Honors - Polynomial and Polynomial Functions Test Review Answer Section 1 15x 5 + 6x 4 2 height: 21 in depth: 5 in 3 6 real zeros and 5 turning points; 0, 1, and 5 4 6x 3 + 8x 2 39x x x 2 14x x 2 18x x 2 12x 44, R even 9 neither 10 neither 11 F 12 F ,± , 2, 3, ± 35i 3, , (7x 10)(x 1) 19 (8x 2 + 5)(3x 5) 20 3x(x 5)(x 3) 21 C 22 The relative maximum is at ( 059, 13) and the relative minimum is at (042, 079) Increasing:, 059ˆ and 042, ˆ Decreasing : 059,042ˆ Domain:, ˆ Range:, ˆ 23 B x 5 + x 4 + x 3 2x 2 + 6x (6x + 1)(2x 5)(x 6) 27 (2x 7)(2x + 7)(x 12) 28 3a + 4b 3 2x + 3 The measure of the width of the rectangle is given by the expression (24a + 4b) 2 9a 2b ( ) Simplify this expression by grouping similar terms and then combining them 1

6 29 There are three turning points 30 The end behavior of the graph is f( x) as x + and f( x) as x It is an even-degree polynomial function The function has four real zeros cm by 8 cm by 2 cm 32 20x 2 40x f(x) = x 3 + 8x x , 1, 3 (multiplicity of 2) As x, f(x) - As x +, f(x) 35 negative, degree 3 36 increasing,01ˆ 25, ˆ decreasing (01, 25) 37 No (use synthetic division to determine if it is a factor) 2