The polynomial f(x) = 10x^3 + 43x^2 + 36x - 9 factors into 10(x - 1/5)(x + 3)(x + 3) with k = 1/5 as a zero
To factor the polynomial f(x) = 10x^3 + 43x^2 + 36x - 9 into linear factors given that k = 1/5 is a zero of f(x), we can use the factor theorem. According to the factor theorem, if k is a zero of f(x), then x - k is a factor of f(x).
Given k = 1/5, we can construct the factor x - 1/5. To find the other factors, we can perform polynomial long division or synthetic division. Performing the division gives us the quadratic quotient 10x^2 + 45x + 45.
Now, factoring the quadratic further, we get 10(x + 3)(x + 3).
Therefore, the factored form of f(x) is 10(x - 1/5)(x + 3)(x + 3).
In summary, f(x) = 10x^3 + 43x^2 + 36x - 9 factors into linear factors as f(x) = 10(x - 1/5)(x + 3)(x + 3) with k = 1/5 being one of the zeros.