Advanced Algebra Trig.
Test Review-Quadratics/Polynomials/Synthetic Division
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Pd. ____ Date ___________________________
Factor the trinomial, or state that the trinomial is prime.
1) x2 + 10x + 21
Determine whether the given quadratic function has a
minimum value or maximum value. Then find the
coordinates of the minimum or maximum point.
9) f(x) = -x 2 - 2x - 5
2) 3x2 + 28x + 32
10) f(x) = 2x 2 - 2x - 4
Factor by grouping. Assume any variable exponents
represent whole numbers.
3) x3 + 2x2 - 5x - 10
11) f(x) = -x 2 - 2x + 6
Factor completely, or state that the polynomial is prime.
4) 4x2 - 16x - 20
12) f(x) = -7x2 - 14x + 7
Factor using the formula for the sum or difference of two
cubes.
5) 8x3 + 1
Solve the problem.
13) The profit that the vendor makes per day by
selling x pretzels is given by the function
P(x) = -0.002x2 + 1.2x - 300. Find the number
Solve the equation by factoring.
6) x2 = x + 12
of pretzels that must be sold to maximize
profit.
Solve the equation by completing the square.
7) x2 - 8x - 3 = 0
14) A person standing close to the edge on top of a
144-foot building throws a baseball vertically
upward. The quadratic function
s(t) = -16t2 + 64t + 144 models the ball's height
above the ground, s(t), in feet, t seconds after it
was thrown. After how many seconds does the
ball reach its maximum height? What is the
maximum height reached? Round to the
nearest tenth, if necessary.
Solve the equation using the quadratic formula.
8) 5x2 + x - 1 = 0
1
Determine whether the function is a polynomial function.
x4 - 3
15) f(x) =
x6
16) f(x) = -17x3 - 9x +
Complete the following:
(a) Use the Leading Coefficient Test to determine the
graph's end behavior.
(b) Find the x-intercepts. State whether the graph crosses
the x-axis or touches the x-axis and turns around at each
intercept.
(c) Find the y-intercept.
(d) Graph the function.
22) f(x) = x2 (x + 3)
3
x
Find the degree of the polynomial function.
3
17) f(x) = 3x - x 4 +
2
Find the zeros of the polynomial function.
18) f(x) = x3 + 7x2 - x - 7
19) f(x) = x3 - 6x2 + 9x
Find the zeros for the polynomial function and give the
multiplicity for each zero. State whether the graph crosses
the x-axis or touches the x-axis and turns around, at each
zero.
20) f(x) = 5(x + 7)(x - 6)2
23) f(x) = x4 - 4x2
21) f(x) = 3(x - 4)(x + 5)3
2
Divide using synthetic division.
27) (x2 + 15x + 56) ÷ (x + 8)
24) f(x) = x3 + 2x2 - x - 2
Solve the problem.
28) Use synthetic division to divide f(x) = x3 - 5x 2
- 12x + 36 by x - 2. Use the result to find all
zeros of f.
25) f(x) = x(x - 1)(x + 2)
Use synthetic division and the Remainder Theorem to
find the indicated function value.
26) f(x) = 2x 3 - 5x2 - 3x + 16; f(-2)
3