Find a cubic polynomial \( P(x) \) with given zeros (roots) that passes through a specified point. Generate random problems, see detailed steps using the Factor Theorem, and visualize the polynomial on a graph.
📐 Polynomial from Zeros and Point
Find cubic polynomial with given zeros through a point
Zeros: \( x = 1, 2, 3 \), Point: \( (0, 6) \)
Find the cubic polynomial in standard form. Click "Show me" for each step.
📖 Step-by-Step Solution
STEP 1: Write the factors corresponding to the given zeros
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STEP 2: Express P(x) as the product of a constant a and the three factors
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STEP 3: Use the given point to find the constant a
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STEP 4: Write the polynomial in standard form
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📊 Graphical Visualization
Polynomial: Green | Zeros (x-intercepts): Red | Given point: Blue
Adjust axis scale to see the polynomial and points clearly.