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Learn how to use synthetic division for polynomial evaluation and division, applying the method to solve polynomial examples and related geometric applications. Understand how to interpret results according to the Remainder Theorem. Explore practical exercises and examples. Practice division and substitution techniques in algebra and geometry.
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Essential Questions • How do we use long division and synthetic division to divide polynomials?
You can use synthetic division to evaluate polynomials. This process is called synthetic substitution. The process of synthetic substitution is exactly the same as the process of synthetic division, but the final answer is interpreted differently, as described by the Remainder Theorem.
Example 1: Using Synthetic Substitution Use synthetic substitution to evaluate the polynomial for the given value.
Example 2: Using Synthetic Substitution Use synthetic substitution to evaluate the polynomial for the given value.
Example 3: Using Synthetic Substitution Use synthetic substitution to evaluate the polynomial for the given value.
Example 4: Using Synthetic Substitution Use synthetic substitution to evaluate the polynomial for the given value.
V h The volume V is related to the area A and the height h by the equation V = A h. Rearranging for A gives A = . x3 – x2 – 6x A(x) = x + 2 Example 5: Geometry Application Write an expression that represents the area of the top face of a rectangular prism when the height is x + 2 and the volume of the prism is x3 – x2 – 6x. The area of the face of the rectangular prism can be represented by A(x)= x2 – 3x.
