Math, asked by sukhjinder389, 9 months ago

Using factor theorem, determine whether g(x) is factor of p(x) in following cases:

a) p(x) = x3 + 3x2 + 5x + 6, g(x) = x + 2

b) p(x) = 2x3 + x2

- 2x - 1, g(x) = x + 1​

Answers

Answered by decentdileep
8

a)P(x) =x^3+3x^2+5x+6

g(x)=x+2=0

g(x)=x=-2

P(-2)=(-2)^3+3(-2)^2+5(-2)+6

P(-2)=-8+3(4)+5(-2)+6

P(-2)=-8+12-10+6

P(-2)=0

P(-2) is a factor of p(x) =x^3+3x^2+5x+6

b)p(x)=2x^3+x^2-2x-1

g(x) =x+1=0

g(x)=x=-1

P(-1)=2(-1)^3+(-1)^2-2(-1)-1

P(-1)=2(-1)+1+2-1

P(-1)=-2+1+2-1

P(-1)=0

P(-1) is a factor of 2x^3+x^2

I hope it's help you

Plz mark my answer as a brainliest answer

Answered by Rose08
24

Answer :-

Using factor theorem, determine whether g(x) is factor of p(x) in following cases :

i] p(x) = x³ + 3x² + 5x + 6 , g(x) = (x + 2)

= Let's find the zero of the polynomial (x + 2),

=> x + 2 = 0

=> x = -2

Putting the value of x in p(x), we get :

=> x³ + 3x² + 5x + 6 = 0

=> (-2)³ + 3 × (-2)² + 5 × (-2) + 6 = 0

=> -8 + 3 × 4 + (-10) + 6 = 0

=> -8 + 12 - 10 + 6 = 0

=> -18 + 18 = 0

=> 0 = 0

Since, we get 0 after putting the value of x and solving the equation, g(x) is a factor of p(x).

__________________________________

ii] p(x) = 2x³ + x² - 2x - 1 , g(x) = (x + 1)

= Let's the find the zero of the polynomial (x + 1),

=> x + 1 = 0

=> x = -1

Putting the value of x in p(x), we get :

=> 2 × (-1)³ + (-1)² - 2 × (-1) - 1 = 0

=> 2 × (-1) + 1 - (-2) - 1 = 0

=> -2 + 1 + 2 - 1 = 0

=> 3 - 3 = 0

=> 0 = 0

Since, we get 0 after putting the value of x and solving the equation, g(x) is a factor of p(x).

Similar questions