For P(x) = 2x^4 – 5x^3+x-10, use synthetic substitution to evaluate P(-2). P(1), and P(2).

P(-2) = 2(-2^4) - 5(-2^3) + (-2) -10

= 2(16) - 5(-8) + (-2) - 10

= 32+40-2-10

= 60

P(1) = 2(1^4) - 4(1^3) + (1) - 10

= 2 - 4 + 1 - 10

= -11

P(2). = 2(2^4) - 5(2^3) + (2) - 10

= 2(16) - 5(8) + 2 - 20

= 32-40+2-10

= -20

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