Polynomial Division 2
Algebra 2
Simplify the following monomial expression.
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2)
Simplify the following polynomial expressions.
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4)
5)
6)
Simplify using long division. Confirm your answer using synthetic division.
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8)
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12)
Use synthetic division to simplify the following expressions.
13) (m - 8), m3 - 7m2 - 14m + 48
14) (a - 2), 2a3 + a2 - 7x - 6
15) (x + 6), x3 - 27x + 54
16) (t + 4), t3 - 12t + 16
Simplify problems 13 - 16 using long division.
17)
19)
18)
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21) Is (x + 2) a factor of x3 + 12x2 + 47x + 60?
22) Is (x + 5) a factor of x3 + 3x2 - 9x + 5?
23) Is (x + 6) a factor of x3 + 11x2 + 36x + 36?
24) Is (x + 4) a factor of x3 - 4x2 - 9x + 36?
Use the signs of a quadratic or cubic polynomial to determine whether the binomial can be a factor?
25) (t + 2), t3 + 6t2 + 12t + 8
26) (v - 3), v3 + 11v2 + 40v + 48
27) (t - 4), t3 + 6t2 + 12t + 8
28) (v + 6), v3 + 11v2 + 40v + 48
Use the constant of a quadratic or cubic polynomial to determine whether the binomial can be a factor?
29) (d - 5), d3 + d2 - 26d + 24
30) (t - 9), t3 + 5t2 - 9t - 45
31) (d - 4), d3 + d2 - 26d + 24
32) (t + 4), t3 + 5t2 - 9t - 45
Determine whether the binomial is a factor of the cubic polynomial. If so, factor the larger polynomial
completely (depress it), and give the x-intercepts of the polynomial function.
33) (t + 3), t3 + t2 - 22t - 40
34) (x - 7), x3 + 15x2 + 74x + 120
35) (b + 4), b3 + 2b2 - 11b - 12
36) (k - 8), k3 - 2k2 - 55k + 56
37) (x - 1), x3 - 3x + 2
38) (x + 3), x3 + 9x2 + 27x + 27
39) (4x + 3), 4x3 - 17x2 + 9x + 18
40) (2v - 5), 2m3 - 7m2 - 19m + 60
41) (x - 6), x3 - 2x2 - 29x + 30
42) (x - 2), x3 - 8x2 - 15x + 54
43) (a + 5), a3 - 5a2 - 29a + 105
44) (t + 5), t3 + t2 - 20t
45) (d - 8), d3 - 6d2 - 16d
46) (v + 9), v3 - 63v + 162
47) (2m + 1), 6m3 + 19m2 + 16m + 4
48) (3x - 2), 3x3 + x2 - 20x + 12