Question

verify division algorithm for the polynomials..p(x)=x³+x²+2x+3 and g(x)= x+2. find p(-2). what do you observe??A​

Answer 1

Answer:

p(-2)=-5

Step-by-step explanation:

I think you're asking about remainder theorem here.

In remainder theorem we equate the divisor's value to 0 and we substitute it in the dividend with the obtained x value.

Since g(x)=x+2;

By remainder theorem

x+2=0

x= -2

We substitute -2 in p(x)

So p(x)=x³+x²+2x+3

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

= -8+4-4+3=-5

As p(-2)'s value is not equal to 0 we can conclude that g(x) will leave a remainder if it divides p(x). If we obtain 0 as a remainder we can conclude that g(x) can divide p(x).