Plug into \( P(x) \): \( P(5) = -2(25) + 20(5) - 30 = -50 + 100 - 30 = 20 \).

["Plug Into ( P(x) ): Step-by-Step Calculation Explained", "Understanding polynomial evaluation is essential in algebra and applied mathematics. One common task is plugging values into a polynomial expression like ( P(x) = -2(25) + 20(5) - 30 ) and computing the result accurately. In this article, we’ll explore how to evaluate ( P(5) ), provide a clear calculation, and explain why this process matters in academic and real-world contexts.", "### What Is ( P(x) )?", "At its core, ( P(x) ) is a polynomial function of one variable ( x ). The specific form used here is:\n[\nP(x) = -2(25) + 20(5) - 30\n]\nWhile this expression appears simple at first glance, evaluating it accurately requires careful attention to operations and order of computation.", "### Why Evaluate ( P(5) )?", "Evaluating polynomials at specific values is fundamental in many fields, including physics, engineering, economics, and computer science. For instance, ( P(x) ) could represent a profit function, a motion equation, or a model predicting outcomes—plugging in ( x = 5 ) helps analyze behavior at that point.", "### Step-by-Step Evaluation of ( P(5) )", "We begin with:\n[\nP(5) = -2(25) + 20(5) - 30\n]", "Step 1: Compute the products inside the parentheses\nMultiply the coefficients with their constants:\n[\n-2 \ imes 25 = -50\n]\n[\n20 \ imes 5 = 100\n]", "Step 2: Rewrite the expression\nSubstitute the computed values back into the polynomial:\n[\nP(5) = -50 + 100 - 30\n]", "Step 3: Apply addition and subtraction from left to right\nFirst, combine (-50 + 100):\n[\n-50 + 100 = 50\n]\nNow add (-30):\n[\n50 - 30 = 20\n]", "Thus,\n[\nP(5) = 20\n]", "### Final Result", "The value of ( P(5) ) is 20, confirmed by systematic substitution and arithmetic.", "### Takeaways", "- Evaluating polynomials involves substituted arithmetic followed by ordered operations (PEMDAS/BODMAS).\n- Clear step-by-step breakdown prevents errors and builds confidence in algebra.\n- Real-world applications depend on such precise computations to model and predict outcomes accurately.", "### Want to Master Polynomials?", "For deeper understanding, practice evaluating expressions with different variables and coefficients. Use tools like calculators or software to verify results, but always verify by breaking down each term.", "Understanding ( P(5) = 20 ) is more than a number—it’s a building block for solving equations, analyzing graphs, and applying math across disciplines. Keep practicing, and soon evaluating polynomials will become second nature.", "---", "Keywords: evaluate polynomial, plug in values, ( P(5) ) calculation, algebraic computation, mathematical example, step-by-step math, polynomial evaluation", "Meta Description: Learn how to evaluate ( P(5) ) for the polynomial ( P(x) = -2(25) + 20(5) - 30 ), with clear step-by-step arithmetic and real-world significance. Perfect for students and practitioners."]