Final Answer:
To find P(x - 4), substitute (x - 4) into the expression for P(a). Therefore, P(x - 4) = (x - 4)³ - 5.
P(x - 4) = (x - 4)³ - 5
Step-by-step explanation:
To find P(x - 4), substitute (x - 4) into the expression for P(a). Therefore, P(x - 4) = (x - 4)³ - 5. Now, let's break down the calculation.
First, expand the cube term:
\[ (x - 4)³ = (x - 4)(x - 4)(x - 4) \]
\[ = (x - 4)(x² - 8x + 16) \]
\[ = x³ - 8x² + 16x - 4x² + 32x - 64 \]
\[ = x³ - 12x² + 48x - 64 \]
Now, substitute this expanded expression back into P(x - 4):
\[ P(x - 4) = x³ - 12x² + 48x - 64 - 5 \]
Combine like terms:
\[ P(x - 4) = x³ - 12x² + 48x - 69 \]
So, the final answer is P(x - 4) = x³ - 12x² + 48x - 69. This expression represents the polynomial obtained by substituting (x - 4) into the original function P(a). It follows the general form of a cubic polynomial, and the coefficients indicate the impact of the transformation on the original function.