Question

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Please solve this sum


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Answer 1

$x^{3}$Hi :D i hope ur doing well!

Step-by-step explanation:

Q.2 Here, p(x)= x^3+3x^2+1

And, g(x)=2x+1=0

               x= -1/2

Now,

p(-1/2)= (-1/2)^3 + 3(-1/2)^2 +1

= -1/8+ 3/2 + 1

Now taking the L.C.M we get,

= -1/8 + 12/8 +8/8

= 19/8

Therefore, the remainder is 19/8

Q.3  Here, p(x)= $x^{4}$ + $x^{3}$+ $x^{2}$  + x + 1

And g(x) = x+1 =0

                 x= -1

To find whether g(x) is a factor of p(x),

p(-1)= $(-1)^{4}$ + $(-1)^{3}$ + $(-1)^{2}$ + (-1) +1

= -1 - 1  + 1

= -2 + 1

= -1

As the remainder is not zero so g(x) is not a factor of p(x)

Q.4 Here, p(x)= $x^{3}$ - $4x^{2}$ +x +6

And g(x)= x-3 = 0

                x=3

To find whether g(x) is a factor of p(x),.

p(3)= $3^{3}$ - 4($3^{2}$) + 3 +6

= 27 - 36 + 9

=36 - 36

=0

Here the remainder is zero.

Hence g(x) is a factor of p(x)

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