Respuesta :

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

carlosego

Answer: 5 (The second option).


Step-by-step explanation:

1. To divide [tex]f(x)=x^4-3x^3+7x-1[/tex] by [tex](x-2)[/tex] you must complete the polynomial with the missing term [tex]0x^{2}[/tex]:

[tex]f(x)=x^4-3x^3+0x^{2}+7x-1[/tex]

2. Write the coefficients of the polynomial and solve for [tex]x[/tex] in the deminator to find the number to write in the division:

[tex]x-2=0\\x=2[/tex]

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.

 


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