Review Test Polynomials Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the function is a polynomial function. 1) f(x) = 7 - 1 x 3 1) A) Yes B) No 2) f(x) = 4 x 5 - x 2 + 3 2) A) Yes B) No 3) f(x) = Δ x 4 + 3 x 3 + 7 3) A) No B) Yes Find the x - intercepts of the polynomial function. State whether the graph crosses the x - axis, or touches the x - axis and turns around, at each intercept. 4) f(x) = x 4 - 49 x 2 4) A) 0, touches the x - axis and turns around; 7 , crosses the x - axis; - 7 , crosses the x - axis B) 0, touches the x - axis and turns around; 49 , touches the x - axis and turns around C) 0, crosses the x - axis; 7 , crosses the x - axis; - 7 , crosses the x - axis D) 0, touches the x - axis and turns around; 49 , crosses the x - axis 5) x 5 - 19 x 3 + 48 x = 0 5) A) 0, touches the x - axis and turns around; 4 , crosses the x - axis; - 4 , crosses the x - axis; 3 , crosses the x - axis; - 3 , crosses the x - axis B) 0, touches the x - axis and turns around; 16 , touches the x - axis and turns around; 3 , touches the x - axis and turns around C) 0, crosses the x - axis; 4 , crosses the x - axis; - 4 , crosses the x - axis; 3 , crosses the x - axis; - 3 , crosses the x - axis D) 0, crosses the x - axis; 16 , touches the x - axis and turns around; 3 , touches the x - axis and turns around 6) f(x) = - x 2 (x + 9 )( x 2 - 1) 6) A) 0, touches the x - axis and turns around; - 9 , crosses the x - axis; - 1, crosses the x - axis; 1, crosses the x - axis B) 0, touches the x - axis and turns around; 9 , crosses the x - axis; - 1, touches the x - axis and turns around; 1, touches the x - axis and turns around C) 0, touches the x - axis and turns around; - 9 , crosses the x - axis; 1, touches the x - axis and turns around D) 0, crosses the x - axis; - 9 , crosses the x - axis; - 1, crosses the x - axis; 1, crosses the x - axis 1
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Review Test Polynomials
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine whether the function is a polynomial function.
1) f(x) = 7 -1x3 1)
A) Yes B) No
2) f(x) =4
x5 - x2 + 3 2)A) Yes B) No
3) f(x) = x4 + 3x3 + 7 3)A) No B) Yes
Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis andturns around, at each intercept.
4) f(x) = x4 - 49x2 4)A) 0, touches the x-axis and turns around;
7, crosses the x-axis;-7, crosses the x-axis
B) 0, touches the x-axis and turns around;49, touches the x-axis and turns around
C) 0, crosses the x-axis;7, crosses the x-axis;-7, crosses the x-axis
D) 0, touches the x-axis and turns around;49, crosses the x-axis
5) x5 - 19x3 + 48x = 0 5)A) 0, touches the x-axis and turns around;
4, crosses the x-axis;-4, crosses the x-axis;
3, crosses the x-axis;- 3, crosses the x-axis
B) 0, touches the x-axis and turns around;16, touches the x-axis and turns around;3, touches the x-axis and turns around
C) 0, crosses the x-axis;4, crosses the x-axis;-4, crosses the x-axis;
3, crosses the x-axis;- 3, crosses the x-axis
D) 0, crosses the x-axis;16, touches the x-axis and turns around;3, touches the x-axis and turns around
6) f(x) = -x2(x + 9)(x2 - 1) 6)A) 0, touches the x-axis and turns around;
-9, crosses the x-axis;-1, crosses the x-axis;1, crosses the x-axis
B) 0, touches the x-axis and turns around;9, crosses the x-axis;-1, touches the x-axis and turns around;1, touches the x-axis and turns around
C) 0, touches the x-axis and turns around;-9, crosses the x-axis;1, touches the x-axis and turns around
D) 0, crosses the x-axis;-9, crosses the x-axis;-1, crosses the x-axis;1, crosses the x-axis
3, touches the x-axis and turns around;-9, crosses the x-axis
B) 0, crosses the x-axis;-3, touches the x-axis and turns around;9, crosses the x-axis
C) 0, touches the x-axis and turns around;3, crosses the x-axis;9, crosses the x-axis
D) 0, touches the x-axis and turns around;-3, touches the x-axis and turns around;9, crosses the x-axis
Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behaviorto match the function with its graph.
8) f(x) = -4x2 - 2x + 1 8)A) rises to the left and rises to the right B) falls to the left and falls to the right
C) rises to the left and falls to the right D) falls to the left and rises to the right
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9) f(x) = -6x3 - 2x2 + 3x + 2 9)A) rises to the left and falls to the right B) falls to the left and falls to the right
C) rises to the left and rises to the right D) falls to the left and rises to the right
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10) f(x) = 2x4 - 4x2 10)A) rises to the left and falls to the right B) rises to the left and rises to the right
C) falls to the left and falls to the right D) falls to the left and rises to the right
Use the Leading Coefficient Test to determine the end behavior of the polynomial function.11) f(x) = -4x4 + 3x3 + 4x2 + 3x + 5 11)
A) rises to the left and falls to the right B) falls to the left and rises to the rightC) rises to the left and rises to the right D) falls to the left and falls to the right
12) f(x) = -3x3 - 2x2 + 3x - 3 12)A) rises to the left and falls to the right B) rises to the left and rises to the rightC) falls to the left and rises to the right D) falls to the left and falls to the right
13) f(x) = (x + 2)(x + 3)(x + 5)3 13)A) falls to the left and rises to the right B) rises to the left and falls to the rightC) rises to the left and rises to the right D) falls to the left and falls to the right
14) f(x) = -x2(x - 1)(x + 2) 14)A) falls to the left and falls to the right B) falls to the left and rises to the rightC) rises to the left and rises to the right D) rises to the left and falls to the right
Find the zeros of the polynomial function.15) f(x) = x3 + 2x2 - x - 2 15)
A) x = - 2, x = 2 B) x = 4C) x = -1, x = 1, x = - 2 D) x = 1, x = - 2, x = 2
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16) f(x) = x3 + 5x2 - 4x - 20 16)A) x = 5, x = -2, x = 2 B) x = -5, x = -2, x = 2C) x = -2, x = 2 D) x = -5, x = 4
Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses thex-axis or touches the x-axis and turns around, at each zero.
7, multiplicity 1, crosses the x-axis-6, multiplicity 1, crosses the x-axis
B) 0, multiplicity 1, crosses the x-axis- 7, multiplicity 1, crosses the x-axis6, multiplicity 1, crosses the x-axis
C) - 7, multiplicity 2, touches the x-axis and turns around6, multiplicity 1, crosses the x-axis
D) 0, multiplicity 1, touches the x-axis and turns around;- 7, multiplicity 1, touches the x-axis and turns around;6, multiplicity 1, touches the x-axis and turns around
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Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or -1 and makethe degree of the function as small as possible.
21) Crosses the x-axis at -4, 0, and 2; lies below the x-axis between -4 and 0; lies above the x-axisbetween 0 and 2.
Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots.53) 4x3 - 23x2 + 26x + 8 = 0 53)
A) 14
, 2, -4 B) 1, -1, 2 C) -14
, 2, 4 D) - 1, -1, -2
54) 2x3 - x2 - 12x + 6 = 0 54)
A) {2, 6, - 6} B) {-2, 6, - 6} C) {- 12
, 6, - 6} D) {12
, 6, - 6}
55) 2x4 - 19x3 + 74x2 - 127x + 78 = 0 55)
A) {2, -32
, 2 + 3i, 2 - 3i} B) {-2, 32
, 3 + 2i, 3 - 2i}
C) {2, 32
, 3 + 2i, 3 -2i} D) {-2, -32
, 2 + 3i, 2 - 3i}
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56) 3x4 + 16x3 + 56x2 + 56x + 13 = 0 56)
A) {1, +13
, -3 + 2i, -3 - 2i} B) {-1, +13
, -3 + 2i, -3 - 2i}
C) {1, -13
, -2 + 3i, -2 - 3i} D) {-1, -13
, -2 + 3i, -2 - 3i}
Find an nth degree polynomial function with real coefficients satisfying the given conditions.57) n = 3; - 4 and i are zeros; f(-3) = 60 57)
Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function.59) f(x) = -5x7 + x3 - x2 + 9 59)
A) 2 or 0 positive zeros, 2 or 0 negative zeros B) 2 or 0 positive zeros, 3 or 1 negative zerosC) 3 or 1 positive zeros, 3 or 1 negative zeros D) 3 or 1 positive zeros, 2 or 0 negative zeros
60) f(x) = 6x5 - 4x2 + x + 4 60)A) 3 or 1 positive zeros, 3 or 1 negative zeros B) 2 or 0 positive zeros, 1 or 0 negative zerosC) 2 or 0 positive zeros, 2 or 0 negative zeros D) 2 or 0 positive zeros, 1 negative zero
61) f(x) = x5 - 1.5x4 - 13.76x3 + 3x2 + 34.42x - 15.397 61)A) 3 or 1 positive zeros, 2 or 0 negative zeros B) 2 or 0 positive zeros, 3 or 1 negative zerosC) 3 or 1 positive zeros, 3 or 1 negative zeros D) 2 or 0 positive zeros, 2 or 0 negative zeros
62) f(x) = 6x8 - 9x7 + x6 - 3x + 18 62)A) 4, 2 or 0 positive zeros, no negative zeros B) 4 or 2 positive zeros, no negative zerosC) 4 positive zeros, no negative zeros D) 4, 2 or 0 positive zeros, 1 negative zeros