Question

Noemi wants to divide 2x^2−x+4 by x−5 using synthetic division.Which answer shows the correct process? A synthetic division diagram with 5 in the upper left box and contains 3 rows and 3 columns of numbers. Row 1 contains coefficients 2, negative 1, and 4. Row 2, beginning under negative 1 from row 1, contains coefficients 10 and 45. Row 3, which is under the horizontal addition bar and aligned with each column, contains the values 2, 9, and 49. A synthetic division diagram with negative 5 in the upper left box and contains 3 rows and 3 columns of numbers. Row 1 contains coefficients 2, negative 1, and 4. Row 2, beginning under negative 1 from row 1, contains coefficients negative 10 and 55. Row 3, which is under the horizontal addition bar and aligned with each column, contains the values 2, negative 11, and 59. A synthetic division diagram with negative 5 in the upper left box and contains 3 rows and 3 columns of numbers. Row 1 contains coefficients 2, negative 1, and 4. Row 2, beginning under negative 1 from row 1, contains coefficients negative 10 and negative 45. Row 3, which is under the horizontal addition bar and aligned with each column, contains the values 2, 9, and negative 41. A synthetic division diagram with 5 in the upper left box and contains 3 rows and 3 columns of numbers. Row 1 contains coefficients 2, negative 1, and 4. Row 2, beginning under negative 1 from row 1, contains coefficients 10 and negative 55. Row 3, which is under the horizontal addition bar and aligned with each column, contains the values 2, negative 11, and negative 51.

Answer 1

Answer:

2x + 9 with a remainder of 45.

Step-by-step explanation:

If the divisor is x-5, use the divisor 5 in synthetic div.

Taking the coefficients 2, -1 and 4 from the dividend, we get:

    ------------------

5  /    2    -1    4

              10   45  

    --------------------

       2       9   49

This tells us that the quotient is 2x + 9 and that the remainder is 49.