Question

find the product.

1. (t - 2)(t² - 5t + 1)

Explanation:

Step1: Apply distributive property (FOIL for polynomials)

Multiply \( t \) by each term in \( t^2 - 5t + 1 \): \( t \cdot t^2 = t^3 \), \( t \cdot (-5t) = -5t^2 \), \( t \cdot 1 = t \).
Then multiply \( -2 \) by each term in \( t^2 - 5t + 1 \): \( -2 \cdot t^2 = -2t^2 \), \( -2 \cdot (-5t) = 10t \), \( -2 \cdot 1 = -2 \).

Step2: Combine like terms

Combine the \( t^2 \) terms: \( -5t^2 - 2t^2 = -7t^2 \).
Combine the \( t \) terms: \( t + 10t = 11t \).
Now, write all terms together: \( t^3 - 7t^2 + 11t - 2 \).

Answer:

\( t^3 - 7t^2 + 11t - 2 \)