Check whether g(x) is a factor of p(x) by dividing p(x) by g(x) in below given data :
p(x)= $x^{5} + 11 x - 12$ , g(x) = $x^{2} - 2 x + 3$

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Solution

Given Data:
Dividend : $x^{5} + 11 x - 12$
Divisor : $x^{2} - 2 x + 3$
Using long division method,
Here, remainder = $0$ ,so g(x) is a factor of p(x).
Hence, g(x) is a factor of p(x).

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Similar questions

Q. Using factor theorem, show that g(x) is a factor of p(x), when
p(x) = 69 + 11x – x² + x³, g(x) = x + 3

Q. Using the remainder theorem, find the remainder, when p(x) is divided by g(x), where

p (x) = 2 x^{3} + 3 x^{2} - 11 x - 3, g (x) = (x + \frac{1}{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 $x^{3}$ + $x^{2}$ −2x−1,g(x)=x+1
(ii) p(x)= $x^{3}$ +3 $x^{2}$ +3x+1,g(x)=x+2
(iii) p(x)= $x^{3}$ −4 $x^{2}$ +x+6,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

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

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Check whether g(x) is a factor of p(x) by dividing p(x) by g(x) in below given data :p(x)= x5+11x-12, g(x) = x2-2x+3

Given Data:Dividend : x5+11x-12Divisor : x2-2x+3Using long division method,Here, remainder = 0,so g(x) is a factor of p(x).Hence, g(x) is a factor of p(x).

Check whether g(x) is a factor of p(x) by dividing p(x) by g(x) in below given data :
p(x)= $x^{5} + 11 x - 12$ , g(x) = $x^{2} - 2 x + 3$

Given Data:
Dividend : $x^{5} + 11 x - 12$
Divisor : $x^{2} - 2 x + 3$
Using long division method,
Here, remainder = $0$ ,so g(x) is a factor of p(x).
Hence, g(x) is a factor of p(x).