Question

Factor f(t) into linear factors given that k is a zero of f(t). f(t)=3t^(3)+7t^(2)-155t+225;k=5

Answer 1

To factor the polynomial f(t) = 3t^3 + 7t^2 - 155t + 225 into linear factors given that k = 5 is a zero of the polynomial, you can use synthetic division or long division to find the resulting quadratic equation. Then, use the quadratic formula to find the remaining roots.

Step-by-step explanation:

To factor the polynomial f(t) = 3t^3 + 7t^2 - 155t + 225 into linear factors given that k = 5 is a zero of the polynomial, you can use synthetic division or long division to find the resulting quadratic equation. Then, use the quadratic formula to find the remaining roots.

First, we divide f(t) by (t - k), which gives us a quotient of 3t^2 + 22t - 45. This quadratic equation can be factored as (t - 3)(t + 15). So the factored form of f(t) is f(t) = (t - 5)(t - 3)(t + 15).