Unit 5 Test Study Guide - Polynomial Functions. Factor each polynomial below completely.
Understand the Problem
The question involves factoring polynomials and performing polynomial operations. It seems to outline various tasks associated with polynomial functions, requiring simplification or complete factorization of the given expressions.
Answer
The expression \( 216ap - p^2 \) factors to \( p(216a - p) \).
Answer for screen readers
The final factored form of the expression ( 216ap - p^2 ) is ( p(216a - p) ).
Steps to Solve
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Identify the Expression to Factor We will focus on one of the expressions provided in the image. For example, let's choose the expression ( 216ap - p^2 ).
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Factor Out Common Terms Look for common factors in the expression. Both terms share ( p ): $$ 216ap - p^2 = p(216a - p) $$
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Re-examine the Remaining Polynomial Check if the polynomial ( 216a - p ) can be factored further. In this case, it cannot be factored more simply since there are no further common factors or special forms.
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Final Factored Form The complete factored form of the original expression is: $$ p(216a - p) $$
The final factored form of the expression ( 216ap - p^2 ) is ( p(216a - p) ).
More Information
Factoring polynomials is crucial for simplifying expressions, solving equations, and understanding polynomial behavior. The ability to factor helps identify roots and analyze function graphs.
Tips
- Forgetting to check for common factors in all terms.
- Incorrectly assuming a polynomial cannot be factored further without checking.
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