Determine whether the statement is true or false. If P(x) = (x − 8) (x + 1)³, then the graph of the polynomial function y = P(x) crosses the x-axis at (8,0). Choose the correct answer below. ОА. ○ B. ○ C. O D. 6 The statement is true because (x-8)° is a factor of the given polynomial function P(x), and the exponent, 6 is even. Thus, the graph crosses the x-axis at (0,8). The statement is false because (x - 8) is a factor of the given polynomial function P(x), and the exponent, 6 is odd. Thus, the graph is tangent to the x-axis at (0,8). 6 The statement is false because (x-8)° is a factor of the given polynomial function P(x), and the exponent, 6 is even. Thus, the graph is tangent to the x-axis at (8,0). The statement is true because (x-8) is a factor of the given polynomial function P(x), and the exponent, 6 is odd. Thus, the graph crosses the x-axis at (8,0).

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.5: Zeros Of Polynomial Functions
Problem 80E
Question
Determine whether the statement is true or false.
If P(x) = (x − 8) (x + 1)³, then the graph of the polynomial function y = P(x) crosses the x-axis at (8,0).
Choose the correct answer below.
ОА.
○ B.
○ C.
O D.
6
The statement is true because (x-8)° is a factor of the given polynomial function P(x), and the exponent, 6
is even. Thus, the graph crosses the x-axis at (0,8).
The statement is false because (x - 8) is a factor of the given polynomial function P(x), and the exponent, 6
is odd. Thus, the graph is tangent to the x-axis at (0,8).
6
The statement is false because (x-8)° is a factor of the given polynomial function P(x), and the exponent, 6
is even. Thus, the graph is tangent to the x-axis at (8,0).
The statement is true because (x-8) is a factor of the given polynomial function P(x), and the exponent, 6
is odd. Thus, the graph crosses the x-axis at (8,0).
Transcribed Image Text:Determine whether the statement is true or false. If P(x) = (x − 8) (x + 1)³, then the graph of the polynomial function y = P(x) crosses the x-axis at (8,0). Choose the correct answer below. ОА. ○ B. ○ C. O D. 6 The statement is true because (x-8)° is a factor of the given polynomial function P(x), and the exponent, 6 is even. Thus, the graph crosses the x-axis at (0,8). The statement is false because (x - 8) is a factor of the given polynomial function P(x), and the exponent, 6 is odd. Thus, the graph is tangent to the x-axis at (0,8). 6 The statement is false because (x-8)° is a factor of the given polynomial function P(x), and the exponent, 6 is even. Thus, the graph is tangent to the x-axis at (8,0). The statement is true because (x-8) is a factor of the given polynomial function P(x), and the exponent, 6 is odd. Thus, the graph crosses the x-axis at (8,0).
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