Question

Using remainder theorem, check whether p(x) is a multiple of g(x) or not for the
following polynomials:- P(x) = 2x3 +11x2
-4x + 5, g(x) = 2x + 1 .

Answer 1

Answer:

NO

Step-by-step explanation:

A.T.Q.

p(x) = 2*3 + 11*2 - 4x + 5

= 6 + 22 - 4x + 5

= 33 - 4x

g(x) = 2x + 1

Now, we can say that p(x) is a multiple of g(x) if

p(Root Of g(x)) = 0

Also,

Root Of g(x) = -1/2 (because 2(-1/2) + 1 = 0)

Therefore,

p(-1/2) = 33 - 4(-1/2)

= 33 +  2

= 35

And,

35 is NOT equal to zero, therefore, we can say that p(x) is NOT a multiple of g(x)

Answer 2

Answer:

NO

Step-by-step explanation:

A.T.Q.

p(x) = 2*3 + 11*2 - 4x + 5

= 6 + 22 - 4x + 5

= 33 - 4x

g(x) = 2x + 1

Now, we can say that p(x) is a multiple of g(x) if

p(Root Of g(x)) = 0

Also,

Root Of g(x) = -1/2 (because 2(-1/2) + 1 = 0)

Therefore,

p(-1/2) = 33 - 4(-1/2)

= 33 +  2

= 35

And,

35 is NOT equal to zero, therefore, we can say that p(x) is NOT a multiple of g(x