Polynomial In Standard Form Worksheet Page 2
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13.) The volume of a cube can be modeled by the equation x
– 8 = 0, where x is the length of the side of the cube.
Find x.
14.) A polynomial equation with rational coefficients has the roots 1 + √ 3 and 3 − √ 2. Find two additional roots.
15.) Use the Rational Root Theorem to list all possible
16.) State the number of complex roots, the possible
3
rational roots for 2x
– 5x + 4 = 0.
number of real roots, and the possible rational roots for
7
5
3
x
– 2x
– 4x
– 2x – 1 = 0.
3
2
17.) Find all of the roots of x
+ x
+ 3x + 3 = 0
18.) List all possible rational roots. Find all of the roots (by hand- show your work). Consider end behavior. Use your
y
5
calculator to find relative extrema. Sketch the graph of the polynomial.
4
3
3
2
P(x) = 2x
+ 7x
– 5x – 4
2
1
–5
–4
–3
–2
–1
1
2
3
4
5
x
–1
–2
–3
–4
–5
Solve by factoring. Graph the quadratic function. Identify the vertex, axis of symmetry, x-intercept(s), y-intercept,
y
and the max/min value.
8
2
19.) x
+ 6x + 8 = 0
6
4
Vertex:_____
2
a of s: _____
O
–8
–6
–4
–2
2
4
6
8
x
x-int: ____________
–2
y – int: _____
–4
–6
max/min: ______
–8
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