Question

What remainder is represented by the synthetic division below?

–5
0
1
2

Answer 1

Synthetic divisions are used to divide polynomials.

The remainder of the synthetic division is 0

In a synthetic division, the remainder of the division is the digit at the bottom right.

From the attached figure that represents the synthetic division, the digit at the bottom right is 0

Hence, the remainder is 0

See attachment for illustration

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Answer 2

Using concepts of synthetic division, it is found that the remainder is of 0.

The coefficients of the polynomial that is the result of the division is given at the bottom-row.

• Thus, the result is $2x^2 + 1$, with a remainder of 0.

• At the top row, there are the coefficients of the original polynomial, which is $2x^3 + 10x^2 + x + 5$.

• Since -5 is at the far left box, the polynomial is being divided by $x + 5$

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