Question

What is the remainder of (4x3-20X -50)/(x-3) ? Show all necessary stepS

Answer 1

To know the remainder, let's perform the operation using Synthetic Division. Here are the steps.

1. Determine the numerical coefficients of the dividend or the numerator.

• 4x³ → 4

,

• 0x² → 0

,

• -20x → -20

,

• -50 → -50

So, the coefficients are 4, 0, -20, and -50 in order of their degrees.

2. Equate the divisor/denominator to zero and solve for x.

`\begin{gathered} x-3=0 \\ x=3 \end{gathered}`

3. Create a table and put the numerical coefficients and value of x in the table like the one below.

4. Then, let's now apply the synthetic division method.

a. Bring down the first coefficient which is 4.

b. Multiply this by 3 and add the result to the next coefficient which is zero.

c. Multiply the result which is 12 by 3 and add the product to the next coefficient.

d. Multiply again the result which is 16 by 3 and add the product to the next coefficient.

The final number in the last cell is -2. Hence, the remainder of the given function is -2.