Question

What is the remainder when the function f(x)=x^4 - 3x^3 +7x - 1 is divided by (x-2)

Answer 1

Answer: Second option. 5}

Solution

To find the remainder of a function when is divided by x-a, you only have to find f(a). In this case we must divide by x-2, then a=2 and we must determine f(2):

x=a=2→f(x)=f(a)=f(2)=(2)^4-3(2)^3+7(2)-1

f(2)=16-3(8)+14-1

f(2)=16-24+14-1

f(2)=5

Answer: the remainder is 5

Answer 2

Answer: 5 (The second option).

Explanation:

1. To divide
`f(x)=x^4-3x^3+7x-1` by
`(x-2)` you must complete the polynomial with the missing term
`0x^(2)`:

`f(x)=x^4-3x^3+0x^(2)+7x-1`

2. Write the coefficients of the polynomial and solve for
`x` in the deminator to find the number to write in the division:

`x-2=0\\x=2`

3. Write the first coefficient under the line, multiply 2 by this coefficient and substract the result with the next coefficient. Multiply the result of the substraction by 2 and repeat the proccedure this with each coefficient:

2 | 1 -3 0 7 -1

1 2 -2 -4 6

___________

-1 -2 3 5

4. The remainder is 5.