Question

question 19 of 25
which of the following shows the division problem below in synthetic division form?
\\(\frac{7x^3 - 2x + 4}{x + 3}\\)
\\(\bigcirc\\) a. \\(-3\overline{\smash{)}7\\ \\ 2\\ \\ 4\\)
\\(\bigcirc\\) b. \\(-3\overline{\smash{)}7\\ \\ -2\\ \\ 4\\)
\\(\bigcirc\\) c. \\(3\overline{\smash{)}7\\ \\ 2\\ \\ 4\\)
\\(\bigcirc\\) d. \\(3\overline{\smash{)}7\\ \\ -2\\ \\ 4\\)

Explanation:

Step1: Identify divisor root

Divisor is $x+3$, so root is $-3$.

Step2: List polynomial coefficients

Polynomial $7x^3 + 0x^2 -2x +4$ has coefficients $7,0,-2,4$. (Note: The original problem's polynomial may have a typo in the image, but based on the options, assume the quadratic term is missing, but the options only show three coefficients—likely a simplification where the quadratic coefficient 0 is omitted in the options. The linear coefficient is $-2$ as in the polynomial.)

Step3: Match with options

Root is $-3$, coefficients are $7,-2,4$ (omitting 0 for the missing term in options).

Answer:

B. $-3\vert7\ -2\ 4$