For zeroes of r1,r2,r3, the factors of the function, f(x) are
(x-r1)(x-r2)(x-r3)
zeroes of -3,-5,2
(x-(-3))(x-(-5))(x-2)=
(x+3)(x+5)(x-2)
f(x)=(x+3)(x+5)(x-2)
expanded
f(x)=x³+6x²-x-30
Answer:
A factor of f(x) is (x + 1).
Step-by-step explanation:
When we put x+1= 0 then we get the value x= -1
This value is then put into the function to find out whether it is a root or not. For a root to exist it must not have a remainder or the remainder must be zero.
Suppose the function is
F(x)= 2x³ - 42x - 40
f(-1)= 2(-1)³ - 42(-1) - 40
f(-1)= -2 + 42- 40
f(-1)= 0
This gives -1 as the root of the function.
One could use the relation

where

are two vectors,

denotes the norm of that vector, and

is the angle between the two vectors.
Then the two vectors will be parallel if

or

.