Using factor theorem, show that g(x) is a factor of p(x), when

Question:

Using factor theorem, show that g(x) is a factor of p(x), when

$p(x)=2 x^{3}+7 x^{2}-24 x-45, g(x)=x-3$

 

Solution:

Let:

$p(x)=2 x^{3}+7 x^{2}-24 x-45$

Now,

$x-3=0 \Rightarrow x=3$

By the factor theorem, (-">- 3) is a factor of the given polynomial if p(3) = 0.
Thus, we have:

$p(3)=\left(2 \times 3^{3}-7 \times 3^{2}-24 \times 3-45\right)$

$=(54+63-72-45)$

$=0$

Hence, (-">- 3) is a factor of the given polynomial.

 

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