1. Use the factor theorem or rational root theorem to find the roots of

1. Use the factor theorem or rational root theorem to find the roots of

Graph Polynomials & Factor and Rational Root Theorem Worksheet
1. Use the factor theorem or rational root theorem to find the roots of the polynomials.
a) x3  x2  10 x  8
b) x3  13x  12
c) x3  5x2  2 x  24
d) x3  6 x2  3x  10
e) 3x3  4 x2  17 x  6
f) 2 x3  3x2  8x  12
Graph Polynomials & Factor and Rational Root Theorem Worksheet
2. Let P( x)  x3  2 x 2  x  2
a.
b.
c.
d.
Determine whether x – 1 is a factor of P(x)
How many zeros does this function have and name them.
Write the polynomial in factored form.
Graph the function.
3. Write a polynomial function in standard form with the given zeros
a. -2, -2, 5
b. -1, 0, 4
c. -3, -1, 2
Graph Polynomials & Factor and Rational Root Theorem Worksheet
4. Write the polynomial in standard form
a.
f ( x)  ( x  3)( x  4)( x  5)
b. f ( x)  ( x  3)2 ( x  1)
Graph Polynomials & Factor and Rational Root Theorem Worksheet
5. Graph each function. Determine its zeros and their multiplicity (how many times the
factor appears).
a. f ( x)  ( x  1)( x  2)( x  3)
b.
f ( x)  ( x  4)2
Graph Polynomials & Factor and Rational Root Theorem Worksheet
c. f ( x)  ( x  1)2 ( x  1)( x  2)
6. The volume of a cube is 125 cm3. Find the length of a side.
Graph Polynomials & Factor and Rational Root Theorem Worksheet
7. This 26-by-21 cm rectangle has been divided into two regions. The width of the
unshaded region is x cm, as shown.
a. Express the area of the shaded part
x
as a function of x, and graph it.
21 cm
x
x
x
26 cm
b. Graph the function