Question

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

Answer 1

Answer: 5 (The second option).

Step-by-step 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.

 

Answer 2

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