Find all the real zeros of the function
f(x) = 2x3 - 19x2 + 38x + 24 given that x-4 is a factor.

Zeroes: x=4, x=-1/2, and x=6

Step-by-step explanation:

Use Synthetic Division where x-4=0 to find another factor:

4 | 2 -19 +38 +24

  ___8_-44_-24

    2 -11  -6  |   0

So far, your two factors are x-4 and 2x^2-11x-6.

We can actually factor 2x^2-11x-6 into (2x+1)(x-6), so we have three factors which are (x-4), (2x+1), and (x-6)!

By the Zero Product Property, x=4, x=-1/2, and x=6 are your zeroes.

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