Question

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

a. (x - 7)
b. (x - 3)
c. (x - 1)
d. (x + 2)

2. Which is the factored form of x3 + 6x2 25x + 18 = 0?

a. (x + 1)(x - 3)(x - 6) = 0
b.(x + 1)(x 2)(x + 9) = 0
c. (x - 1)(x - 3)(x - 6) = 0
d. (x - 1)(x - 2)(x + 9) = 0


3. please wtite the missed signes in equation after - next - 6x*2 and in point
b. (x+1)(x ??? 2)(x+9)

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.