Question:
Using factor theorem, show that g(x) is a factor of p(x), when
$p(x)=2 x^{3}+9 x^{2}-11 x-30, g(x)=x+5$
Solution:
Let:
$p(x)=2 x^{3}+9 x^{2}-11 x-30$
Here,
$x+5=0 \Rightarrow x=-5$
By the factor theorem, (x + 5) is a factor of the given polynomial if p (
Thus, we have:
$p(-5)=\left[2 \times(-5)^{3}+9 \times(-5)^{2}-11 \times(-5)-30\right]$
$=(-250+225+55-30)$
$=0$
Hence, (x + 5) is a factor of the given polynomial.
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