Using factor theorem, show that g(x) is a factor of p(x), when
p(x) = 2x³ + 7x² – 24x – 45, g(x) = x – 3

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Solution

Let:
p(x) = 2x³ + 7x² – 24x – 45
Now,
$x - 3 = 0 \Rightarrow x = 3$
By the factor theorem, (x $-$ 3) is a factor of the given polynomial if p(3) = 0.
Thus, we have:
$p (3) = (2 \times 3^{3} - 7 \times 3^{2} - 24 \times 3 - 45) = (54 + 63 - 72 - 45) = 0$
Hence, (x $-$ 3) is a factor of the given polynomial.

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