Find all zeros (real and complex) and factor the polynomial completely.

Question

a) P(x) = x⁴ − 25

 

b) Q(x) = x³ − 7x² + 17x − 15

Answer 1

I will show you the factoring.  Then from there, you should be able to find the zeros.

 

P(x) = (x² - 5)(x² + 5)

P(x) = (x - √5)(x + √5)(x² + 5)

 

 

For Q(x), use synthetic division to find a quadratic and linear factor.

 

 3 | 1       -7       17        -15

 

                3      -12         15

_____________________________

      1       -4        5            0

 

 

Q(x) = (x - 3)(x² - 4x + 5)

        = (x - 3)(x - 5)(x + 1)

 

Now you can find your zeros.