Use the remainder theorem to find P (3) for P(x) = 2x² - 4x^2- 3. Specifically, give the quotient and the remainder for the associated division and the value of P(3).
Quotient= ?
Remainder=?
P (3) = ?

P(2) = 4

Step-by-step explanation:

P(X) = -2X4 + 4X3 - X + 6

Use the remainder theorem to find quotient and remainder and the value of P(2)

First add in any missing exponents:  P(x) = -2x4 + 4x3 + 0x2 -x + 6

Write all the coefficients in a line (including the constant) with the number being solved for off to the left:

Bring down the first coefficient (-2), multiply it by the term in question (2), carry the product up under

the 2nd coefficient and then add down (4-4=0), carry up the sum and repeat process across.  The last

sum is the answer for P(2)

(2)   -2    4    0    -1    6

            -4    0      0  -2

       -2   0    0     -1   4

P(2) = 4

check the  P(2) = -2(24) + 4(23) -2 + 6 = -2(16) +4(8) + 4 = 4    Our answer is correct

The quotient is what we would bet by dividing the original equation by the polynomial (x-2). The

answer is given by the bottom numbers which will begin an one lower exponent than the original.

Quotient is:   -2x3 + 0x2 + 0x -1 = 2x3 - 1

The remainder is:   4/(x-2)

answer:

(-8,7)

explanation:

we know that  

f

(

−

3

)

=

7

therefore, if we wish to get the output as 7, in the function, we need to have our input to be -3.

looking at the function  

f

(

x

+

5

)

, what should the value of x be, such that the input in the function becomes 7?

we simply equate the terms,

x

+

5

=

−

3

x

=

−

8

thus, the point on the new function would be  

(

−

8

,

7

)

then, the surface area of the sphere shown in the image is: 256π sq. units!

step-by-step explanation:

the lateral surface area of a sphere is 2πrh where h=2r.

then:

surface area = 4πr^2.

in this case, r=8 units ⇒ surface area = 4π(8 units)^2. = 256π sq. units!

then, the surface area of the sphere shown in the image is: 256π sq. units!