Question

1. Which binomial is a factor of f(x) = x^4 + 7x^3 - 7x^2 - 43x + 42?

Answer 1

F(x) = x^4 + 7x^3 - 7x^2 - 43x + 42
f(1) = 1^4 + 7(1)^3 - 7(1)^2 - 43(1) + 42 = 1 + 7 - 7 - 43 + 42 = 0
Since f(1) = 0, therefore (x - 1) is factor.