A student attempted to divide 4 x^3+2 x^2+6 x by x+2 synthetically by setting up the division

step 1 If you're dividing 8x to the 6 plus 6x cubed by 2x to the 4th, you would get 8x to the 6 over 2x

A student attempted to divide 4 x^3+2 x^2+6 x by x+2...

A student attempted to divide
$$
4 x^{3}+2 x^{2}+6 x \text { by } x+2
$$
synthetically by setting up the division as follows.
$$- 2)\overline{ 4 26}$$
This is incorrect. WHAT WENT WRONG? Give the correct setup and the answer.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Synthetic Division

Synthetic division is a shortcut method used to divide a polynomial by a binomial of the form x - c. It involves using the zero c of the divisor and performing a sequence of multiplications and additions on the coefficients of the polynomial. The process yields the coefficients of the quotient polynomial and the remainder at the end of the calculation.

Complete Coefficient Setup

When dividing a polynomial, it is essential to include coefficients for every power of x in descending order, even if certain terms are missing. In the given polynomial 4x^3 + 2x^2 + 6x, the constant term is missing, so a coefficient of 0 must be used to correctly set up the synthetic division as [4, 2, 6, 0]. Omitting any coefficient can cause incorrect results.

Correct Selection of the Divisor’s Root

In synthetic division, the number placed to the left of the division setup is the root of the divisor polynomial. Since the divisor here is x + 2, it can be rewritten as x - (-2), so the correct number to use is -2. Failing to use the appropriate value leads to errors in the computation.

Transcript

Please give Ace some feedback