Given that the expression 2x^3 + mx^2 + nx + c leaves the same remainder when divided by x -2 or by x+1 I prove that m+n =-6

Given:

The expression is:

It leaves the same remainder when divided by x -2 or by x+1.

To prove:

Solution:

Remainder theorem: If a polynomial P(x) is divided by (x-c), thent he remainder is P(c).

Let the given polynomial is:

It leaves the same remainder when divided by x -2 or by x+1. By using remainder theorem, we can say that

             ...(i)

Substituting in the given polynomial.

Substituting in the given polynomial.

Now, substitute the values of P(2) and P(-1) in (i), we get

Divide both sides by 3.

Hence proved.

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional

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step-by-step explanation: