f(x) = 3x³ + x² − 20x +12, g(x) = 3x − 2

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Solution

It is given that and

By the factor theorem,

(3x − 2) is the factor of f(x), if

Therefore,

In order to prove that (3x − 2) is a factor of f(x).

It is sufficient to show that

Now,

Hence, (3x − 2) is the factor of polynomial f(x).

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f (x)

f (x) = 3 x^{3} + x^{2} - 20 x + 12, g (x) = 3 x - 2

Use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x)

f(x) = $3 x^{3} + x^{2}$ - 20x + 12, g(x) = 3x - 2

Using factor theorem, show that g(x) is a factor of p(x), when
$p (x) = 3 x^{3} + x^{2} - 20 x + 12, g (x) = 3 x - 2$

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3 x^{3} + x^{2} - 20 x + 12

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