Help please Using the remainder theorem see if (x-2) and (x+5) are factors of the polynomial

X^2+3x-10

See explanations below

Step-by-step explanation:

Given the polynomial function

P(x) = X^2+3x-10

To check whether x-2 and x+5 are factor, we will find x and then show that P(x) = 0

For x-2

x - 2 = 0

x =2

P(2) = 2²+3(2)-10

P(2) = 4+6 -10

P(2) = 10-10

P(2) = 0

Since the remainder is zero, hence x-2 is a factor of the polynomial

Similarly for x+5;

x+5 = 0

x = -5

P(-5) = (-5)²+3(-5)-10

P(-5) = 25-15-10

P(-5) = 10-10

P(-5) = 0

This also shows that x+5 is a factor

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12