(x-3) is a factor of

From the factor theorem, we have

(x – 3) is the factor of f(x) if f(3) = 0

Here, we have

f(3) = 2 × 3³ + 7 × 3² – 24 × 3 - 45

= 54 + 63 – 72 – 45

= 117 – 117

= 0

Therefore,

(x – 3) is a factor of (2x³ + 7x² – 24x – 45)