Question

show that (x+2) is a factor of (x^5+32) using factor theorem​

Answer 1

given, p(x) = x^5 + 32

Zero of x+2 --

x+2 = 0

x = -2

To show x+2 is a factor of (x^5 + 32), put x = -2 in the given polynomial and if p(x) will be equal to zero after putting x = -2 then it would show that x+2 is the factor of p(x)

we get --

-2^5 + 32 = 0

-32 + 32 = 0

0 = 0

Since, after putting x = -2, we got zero, Therefore x + 2 is the factor of p(x)

Answer 2

we have

x+2=0

using factor theorem then

x=-2

p(x)=x^5+32

p(-2)=(-2)^5+32

=-32+32

=0

hence X + 2 is a factor of x power 5 + 32