Question

use synthetic division to find the quotient of $(5x^{3}-3x - 4)div(x - 2)$. quotient: help (formulas) preview my answers submit answers show me another you have attempted this problem 0 times. you have 5 attempts left before new ver you have unlimited attempts remaining. email instructor

Explanation:

Step1: Set up synthetic division

Write the zero of the divisor \(x - 2\) (which is \(2\)) on the left. Then, write the coefficients of the dividend \(5x^{3}+0x^{2}-3x - 4\) (we include \(0\) for the \(x^{2}\) term) in a row: \(5,0,-3,-4\).

Step2: Bring down the first coefficient

Bring down the first coefficient \(5\).

$$\begin{array}{r|rrrr} 2&5&0&-3&-4\\ &&&\\ \hline &5&&& \end{array}$$

Step3: Multiply and add

Multiply the number just brought down (\(5\)) by the zero (\(2\)): \(5\times2 = 10\). Add this to the next coefficient (\(0+10=10\)).

$$\begin{array}{r|rrrr} 2&5&0&-3&-4\\ &&10&&\\ \hline &5&10&& \end{array}$$

Multiply the new number (\(10\)) by \(2\): \(10\times2=20\). Add to the next coefficient (\(-3 + 20=17\)).

$$\begin{array}{r|rrrr} 2&5&0&-3&-4\\ &&10&20&\\ \hline &5&10&17& \end{array}$$

Multiply \(17\) by \(2\): \(17\times 2=34\). Add to the last coefficient (\(-4+34 = 30\)).

$$\begin{array}{r|rrrr} 2&5&0&-3&-4\\ &&10&20&34\\ \hline &5&10&17&30 \end{array}$$

The coefficients of the quotient polynomial (degree is one less than the dividend, so degree \(2\)) are \(5,10,17\) and the remainder is \(30\). The quotient polynomial is \(5x^{2}+10x + 17\).

Answer:

\(5x^{2}+10x + 17\)