Bot GPT 4-o mini To determine the number of turning points for the function \( m(x) = (2x + 5)(x - 3)^3(8x + 1)^5 \), we first need to analyze the degree of the polynomial.
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Identify the degree of each factor:
- \( (2x + 5) \) is of degree 1.
- \( (x - 3)^3 \) is of degree 3.
- \( (8x + 1)^5 \) is of degree 5.
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Calculate the total degree of the polynomial \( m(x) \): \[ \text{Total degree} = 1 + 3 + 5 = 9 \]
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The number of turning points of a polynomial is at most equal to its degree minus 1. Therefore, for our polynomial of degree 9, the maximum number of turning points is: \[ \text{Maximum turning points} = 9 - 1 = 8 \]
Thus, Brandy should include eight at most turning points in her sketch.
The correct answer is: Eight at most.
1 answer