Redwood High School. Department of Mathematics
Honors Advanced Algebra S2 Test #2 Prep wkst 2.
Hard Worker's Name:___________________________________
Use synthetic division to find the quotient and the
remainder.
4) x4 + 81 is divided by x - 3
Find a rational zero of the polynomial function and use it
to find all the zeros of the function. Then Find the x- and
y-intercepts of f(x), end behavior, label the points and
axis, and graph the function.
1) f(x) = x3 + 2x2 - 5x - 6
5) x5 - 4x4 - 10x3 - 10x2 - 15x + 19 div. by x - 6
Factor the polynomial completely, given that the binomial
is a factor.
6) x - 8, x3 - 4x2 - 28x - 32
Use the factor theorem to decide whether or not the second
polynomial is a factor of the first.
7) 9x4 + 35x3 - 4x2 + x + 4; x + 4
2) f(x) = x3 + 6x2 - x - 6
8) Sketch the graph of the polynomial function.
Label clearly both X and Y intercepts
f(x) = 3x3 (x - 1/2)(x - 1)(x +2)5(x +5)4
3) f(x) = 2x3 - 11x2 + 10x + 8
Use synthetic division to find the function value.
9) f(x) = x5 - 10x4 + 16x3 - 3x - 200; find f(-5).
10) f(x) = 4x5 - 4x4 + 3x3 - x + 3; find f(4).
1
14) Sketch the graph of the polynomial function.
Label clearly both X and Y intercepts
f(x) = x8 (x + 2)(x - 2)(x -2)(x -5)4 (x +3)4
Find all the zeros of the polynomial function, then find
the x- and y-intercepts of f(x), end behavior, label the
points and axis, and graph the function.
11) f(x) = 2x3 + 3x2 - 9x - 10
Form a polynomial (write it both in factor and in general
forms) whose zeros and degree are given. Graph the
function
15) Zeros: -1, 1, - 4; degree 3
12) f(x) = x3 + 2x2 - 5x - 6
13) f(x) = x4 + x2 - 90
Find all of the real and imaginary zeros for the polynomial
function.
16) f(x) = x3 - 6x2 + x - 6
17) f(x) = x3 - 3x2 - 36x + 108
18) f(x) = 6x3 + 16x2 + 6x - 4
2
19) Zeros: -2, -3, 3; degree 3
Find the quotient and the remainder.
22) -6x3 - 23x2 - 18x + 9 divided by 2x + 5
23) x4 + 1296 divided by x - 6
24) 8x3 - 30x2 + 41x - 10 divided by -4x + 5
25) x4 + 3x2 + 9 divided by x2 + 1
20) Zeros: 3, multiplicity 2; -3, multiplicity 2;
degree 4
List the potential rational zeros of the polynomial
function. Do not find the zeros.
26) f(x) = 11x3 - x2 + 5
27) f(x) = 6x4 + 4x3 - 3x2 + 2
28) f(x) = -2x3 + 2x2 - 4x + 8
Find the x- and y-intercepts of f(x), end behavior, label
the points and axis, and graph the function.
29) f(x) = (x + 1)(x - 6)(x - 1)2
Find the x- and y-intercepts of f(x), end behavior, label
the points and axis, and graph the function.
21) =- 2(x+ 2)(x- 2)(x+ 2i)(x- 2i)(x + 3)3
3
33) Sketch the graph of the polynomial function.
Label clearly both X and Y intercepts (4
points)
f(x) = 3(x + 2)(x - 1)(x + 3i)(x - 3i)(x +3)2
30) f(x) = -x2 (x + 7)(x2 - 1)
31) f(x) = 3x - x3
Find the x- and y-intercepts of f(x), end behavior, label
the points and axis, and graph the function.
34) f(x) = (2x - 1)(x + 2)2
32) f(x) = 2x2 (x - 4)5
35) f(x) = -3x(x + 1)(x + 2)
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Answer Key
Testname: ADVALG S2 #2 POLYNOMIALS V2.0
1) {-3, -1, 2}
2) {1, -1, -6}
1
3) - , 2, 4
2
4) x3 + 3x2 + 9x + 27; remainder 162
5) x4 + 2x3 + 2x2 + 2x - 3; remainder 1
6) (x - 8)(x + 2)(x + 2)
7) Yes
8)
9) -11,560
10) 3263
5
11) - , -1, 2; f(x) = (2x + 5)(x + 1)(x - 2)
2
12) -3, -1, 2; f(x) = (x + 3)(x + 1)(x - 2)
13) -3, 3; (x + 3)(x - 3)(x2 + 10)
14)
15) f(x) = x3 + 4x2 - x - 4 for a = 1
16) 6, -i, i
17) -6, 3, 6
1
18) - 1, - 2,
3
19) f(x) = x3 - 9x + 2x2 - 18 for a = 1
20) f(x) = x4 - 18x2 + 81
21)
22) -3x2 - 4x + 1; remainder 4
23) x3 + 6x2 + 36x + 216; remainder 2592
24) -2x2 + 5x - 4; remainder 10
25) x2 + 2; remainder 7
26) ±
1
5
,±
, ± 1, ± 5
11
11
27) ±
1
1
1
2
, ± , ± , ± , ± 1, ± 2
6
3
2
3
28) ±
1
, ± 1, ± 2, ± 4, ± 8
2
29) x-intercepts: -1, 1, 6; y-intercept: -6
5
Answer Key
Testname: ADVALG S2 #2 POLYNOMIALS V2.0
30) x-intercepts: -7, -1, 0, 1; y-intercept: 0
31) x-intercepts: 0, 3, - 3; y-intercept: 0
32) x-intercepts: 0, 4; y-intercept: 0
33)
34)
35)
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