Step by Step Solver to Factor a Cubic Polynomial Given One of its Zeros

Factor a cubic polynomial \( P(x) = ax^3 + bx^2 + cx + d \) using the Factor Theorem. Given one zero, find the quadratic factor by synthetic division, then factor completely.

📐 Cubic Polynomial Factorer

Factor \( P(x) = ax^3 + bx^2 + cx + d \) given one zero

\( P(x) = x^3 - 6x^2 + 11x - 6 \), zero: \( x = 1 \)
Factor the cubic polynomial completely. Click "Show me" for each step.

📖 Step-by-Step Solution

STEP 1: Use the given zero to write a factor
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STEP 2: Express P(x) as product of factor and quadratic Q(x)
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STEP 3: Perform synthetic (polynomial) division to find Q(x)
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STEP 4: Factor the quadratic polynomial Q(x)
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STEP 5: Write P(x) in completely factored form
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📊 Graphical Visualization
Polynomial: Green | Zeros (x-intercepts): Red points

Adjust axis scale to see the cubic curve and its zeros clearly.