Question

Use the factor theorem to find the polynomial of degree 4 having zeros x=1+√2, x=1-√2, x=3+i, x=3-i. Assume a lead coefficient of 1.

Answer 1

As you know that the zeros are when x=1+√2, x=1-√2, x=3+i, x=3-i this means your polynomial is (x-(1+√2))(x-(1-√2))(x-(3+i))(x-(3-i)) So you have to multiply all 4 brackets together (after expanding each bracket ofcourse ;))

Answer 2

(x-(1-√2)) for example means x=1-√2 is a zero as if u set the equation to equal 0, x- (1-√2) =0 so x=1-√2