Respuesta :

coolstick
Using long division, we have


        ___________________
2x-1 | 4x^4-10x³+14x²+7x-19

Next, we divide the first term of 2x-1 by the first term of 4x^4-10x³+14x²+7x-19 to get 4x^4/2x=2x³ (since 4/2=2 and to divide exponents you subtract the denominator from the numerator). Next, we put our 2x³ on the top and multiply (2x-1) by that. With the result of (2x-1) and 2x³, we multiply that by -1 and add it to 4x^4-10x³+14x²+7x-19, looking like


        2x³
        ___________________
2x-1 | 4x^4-10x³+14x²+7x-19

       - (4x^4-2x³)
         ____________________
                  -8x³+14x²+7x-19. Repeating the process, we get


        2x³-4x²+5x+6
        ___________________
2x-1 | 4x^4-10x³+14x²+7x-19

       - (4x^4-2x³)
         ____________________
                  -8x³+14x²+7x-19. 
                  -(-8x³+4x²)
       ______________________
                         10x²+7x-19
                        -(10x²-5x)
                        __________
                                 12x-19
                               -(12x-6)
                              _________
                                       -13 as our remainder

Answer:

-13

Step-by-step explanation:

Solving for x , then 2x − 1 = 0 → x =

1

2

. Using the Remainder Theorem, p(

1

2

) will give the remainder. Thus 4(

1

2

)4 − 10(

1

2

)3 + 14(

1

2

)2 + 7(

1

2

) − 19 = −13 .

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