Question

find the value of p for which (X+p) is a factor of x^2+px+ 3-p​

Answer 1

Step-by-step explanation:

For finding the remainder we need to use remainder theorem

Let p(x)=x

2

+px+3−p

As x+p is a factor of p(x), we need to equate it to 0 and put that value of x in p(x).

So, x+p=0

or, x=−p

As, −p is a zero of p(x), so,

p(−p)=(−p)

2

+p(−p)+3−p=0

⇒p

2

−p

2

+3−p=0

or, p=3

Answer 2

Step-by-step explanation:

By corollary 1 to factor theorem, ( x + p ) is a factor of x^2 + px + 3 - p. Hence the required value of p is 3.