Question

Evaluate the polynomial function for the given value of P(x)=5x^(3)-3x^(2)-5; find P(-2)

Answer 1

To find P(-2) for the polynomial function P(x)=5x^3-3x^2-5, substitute -2 for x and simplify. After substitution and simplifying terms, the result is -57.

Step-by-step explanation:

To evaluate the polynomial function P(x) = 5x^3 - 3x^2 - 5 for P(-2), you substitute -2 for every x in the polynomial and then simplify the expression.

1. Substitute -2 for x: P(-2) = 5(-2)^3 - 3(-2)^2 - 5.
2. Simplify the cubic term: 5(-2)^3 becomes 5(-8), which is -40.
3. Simplify the square term: 3(-2)^2 becomes 3(4), which is 12.
4. Combine all terms: -40 - 12 - 5.
5. Complete the calculation: -40 - 12 - 5 = -52 - 5 = -57.

Therefore, the value of P(-2) is -57.