Use the factor theorem to determine whether g(x) is a factor of p(x) in the following case.
$p (x) = 3 x^{3} + 3 x^{2} + 3 x + 1; g (x) = x + 2$

Open in App

Solution

Here $p (x) = 3 x^{3} + 3 x^{2} + 3 x + 1; g (x) = x + 2$
Now
$p (- 2) = 3 (- 2)^{3} + 3 (- 2)^{2} + 3 (- 2) + 1$
$= - 24 + 12 - 6 + 1 = - 30 + 13 = - 17$
$p (- 2) \neq 0$
i.e. $x + 2$ is not a factor of $3 x^{3} + 3 x^{2} + 3 x + 1$

Suggest Corrections

Similar questions

(i) p (x) = 2 x^{3} + x^{2} - 2 x - 1, g (x) = x + 1

(i i) p (x) = x^{3} + 3 x^{2} + 3 x + 1, g (x) = x + 2

(i i i) p (x) = x^{3} - 4 x^{2} + x + 6, g (x) = x - 3

g (x)

p (x)

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

Use the factor theorem to determine whether g(x) is a factor of p(x) in the given expression p(x) = 2x³+ x²- 2x - 1,g(x) = x + 1

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

g (x)

f (x)

f (x) = x^{3} + 3 x^{2} + 3 x + 1, g (x) = x + 1

Join BYJU'S Learning Program