Polynomial Evaluation Given \( p(x)=3 x^{\wedge} 2-2 x+5 \) evaluate \( x=4 \) 25 40 45

To evaluate the polynomial \( p(x) = 3x^2 - 2x + 5 \) at \( x = 4 \), substitute 4 into the equation: \[ p(4) = 3(4)^2 - 2(4) + 5 \] Calculating this gives: \[ p(4) = 3(16) - 8 + 5 = 48 - 8 + 5 = 45. \] So, the answer is 45! Now that you know how to evaluate polynomials, did you know that polynomials are foundational to many areas of mathematics, including calculus and algebra? They can model everything from simple relationships in physics to complex algorithms in computer science! Getting familiar with them opens a world of mathematical exploration. If you want to get better at evaluating polynomials, remember to carefully follow the order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). A common mistake is mixing up the operations or forgetting to apply the exponent correctly! Practice makes perfect!