Valdez Burton

08/05/2024 · Elementary School

Determine whether the statement is true or false. If \( \mathrm{P}(\mathrm{x})=(\mathrm{x}-3)^{2}(\mathrm{x}+6)^{5} \), then the graph of the polynomial function \( \mathrm{y}=\mathrm{P}(\mathrm{x}) \) crosses the x -axis at \( (3,0) \). Choose the correct answer below. A. The statement is true because \( (\mathrm{x}-3)^{2} \) is a factor of the given polynomial function \( \mathrm{P}(\mathrm{x}) \), and the exponent, 2 is odd. Thus, the graph crosses the x -axis at \( (3,0) \). B. The statement is false because \( (\mathrm{x}-3)^{2} \) is a factor of the given polynomial function \( \mathrm{P}(\mathrm{x}) \), and the exponent, 2 is odd. Thus, the graph is tangent to the x -axis at C. The statement is true because \( (\mathrm{x}-3)^{2} \) is a factor of the given polynomial function \( \mathrm{P}(\mathrm{x}) \), and the exponent, 2 is even. Thus, the graph crosses the x -axis at D. The statement is false because \( (\mathrm{x}-3)^{2} \) is a factor of the given polynomial function \( \mathrm{P}(\mathrm{x}) \), and the exponent, 2 is even. Thus, the graph is tangent to the x -axis at \( (3,0) \).