Use the Factor Theorem to determine whether g(x) is a factor of p(x) if $p (x) = 2 x^{3} + x^{2} - 2 x - 1$ and $g (x) = x + 1$

Open in App

Solution

g(x) = x + 1, x = - 1 to be substituted in
$p (x) = 2 x^{3} + x^{2} - 2 x - 1 \Rightarrow p (- 1) = 2 (- 1)^{3} + (- 1)^{2} - 2 (- 1) - 1 = - 2 + 1 + 2 - 1 = 0$
So, g(x) is a factor of p(x).

Suggest Corrections

Similar questions

Using factor theorem, show that g(x) is a factor of p(x), when
$p (x) = 2 x^{3} + 7 x^{2} - 24 x - 45, g (x) = x - 3$

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

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

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

Join BYJU'S Learning Program

Use the Factor Theorem to determine whether g(x) is a factor of p(x) if p(x)=2x3+x2−2x−1 and g(x)=x+1

g(x) = x + 1, x = - 1 to be substituted in p(x)=2x3+x2−2x−1⇒p(−1)=2(−1)3+(−1)2−2(−1)−1=−2+1+2−1=0 So, g(x) is a factor of p(x).

Use the Factor Theorem to determine whether g(x) is a factor of p(x) if $p (x) = 2 x^{3} + x^{2} - 2 x - 1$ and $g (x) = x + 1$

g(x) = x + 1, x = - 1 to be substituted in
$p (x) = 2 x^{3} + x^{2} - 2 x - 1 \Rightarrow p (- 1) = 2 (- 1)^{3} + (- 1)^{2} - 2 (- 1) - 1 = - 2 + 1 + 2 - 1 = 0$
So, g(x) is a factor of p(x).