Use the factor theorem to determine and state whether $g (x)$ is a factor of $p (x)$ in each of the following cases:
$p (x) = x^{3} + 3 x^{2} + 3 x + 1, g (x) = x + 2$

True

No worries! We‘ve got your back. Try BYJU‘S free classes today!

False

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The zero of $g (x) = x + 2$ is $- 2$
Here, $p (x) = x^{3} + 3 x^{2} + 3 x + 1$
Now, Verify whether $- 2$ is a zero of $p (x)$ :
Consider $p (- 2) = (- 2)^{3} + 3 (- 2)^{2} + 3 (- 2) + 1$
$= - 8 + 12 - 6 + 1$
$= - 14 + 13$
$= - 1$
Since, $p (- 2) \neq 0$
Therefore, by Factor theorem, $g (x)$ is not a factor of $p (x)$ .

Suggest Corrections

Similar questions

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:
$(i) p (x) = 2 x^{3} + x^{2} - 2 x - 1, g (x) = x + 1$
$(i i) p (x) = x^{3} + 3 x^{2} + 3 x + 1, g (x) = x + 2$ [4 MARKS]

Q. Question 2
Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:

(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

Q. Use the factor theorem and state whether

g (x)

is a factor of

p (x)

in the following case. State True Or False:

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

Q. In the following case, use factor theorem to find whether

g (x)

is a factor of the polynomial

p (x)

or not.

p (x) = x^{3} - 3 x^{2} + 6 x - 20 g (x) = x - 2

Q. Use the Factor Theorem to determine whether

g (x)

is factor of

f (x)

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

Join BYJU'S Learning Program

Use the factor theorem to determine and state whether g(x) is a factor of p(x) in each of the following cases:p(x)=x3+3x2+3x+1, g(x)=x+2

The zero of g(x)=x+2 is −2Here, p(x)=x3+3x2+3x+1Now, Verify whether −2 is a zero of p(x):Consider p(−2)=(−2)3+3(−2)2+3(−2)+1=−8+12−6+1=−14+13=−1Since, p(−2)≠0Therefore, by Factor theorem, g(x) is not a factor of p(x).

Use the factor theorem to determine and state whether $g (x)$ is a factor of $p (x)$ in each of the following cases:
$p (x) = x^{3} + 3 x^{2} + 3 x + 1, g (x) = x + 2$