Question

use synthetic division to find the result when 2x³ + 3x² - 11x + 6 is divided by x - 1. answer attempt 1 out of 4

Explanation:

Step1: Set up synthetic division

For dividing by \(x - 1\), we use \(r = 1\) (from \(x - r\)). The coefficients of the polynomial \(2x^{3}+3x^{2}-11x + 6\) are \(2\), \(3\), \(-11\), \(6\).
Set up the synthetic division as:

$$
LATEXBLOCK0
$$

Step2: Bring down the leading coefficient

Bring down the \(2\) to the bottom row:

$$
LATEXBLOCK1
$$

Step3: Multiply and add

Multiply the number we just brought down (\(2\)) by \(r = 1\), which gives \(2\times1 = 2\). Add this to the next coefficient (\(3\)): \(3+2 = 5\). Write this in the bottom row:

$$
LATEXBLOCK2
$$

Step4: Multiply and add again

Multiply the new number in the bottom row (\(5\)) by \(r = 1\), which gives \(5\times1=5\). Add this to the next coefficient (\(-11\)): \(-11 + 5=-6\). Write this in the bottom row:

$$
LATEXBLOCK3
$$

Step5: Multiply and add the last time

Multiply the new number in the bottom row (\(-6\)) by \(r = 1\), which gives \(-6\times1=-6\). Add this to the last coefficient (\(6\)): \(6+(-6)=0\). Write this in the bottom row:

$$
LATEXBLOCK4
$$

The bottom row coefficients (excluding the last one which is the remainder) give the quotient polynomial. The remainder is \(0\) (which makes sense since \(x - 1\) is a factor). The quotient polynomial has degree one less than the original polynomial. So the quotient is \(2x^{2}+5x - 6\) and the remainder is \(0\). Since the remainder is \(0\), the result of the division \(2x^{3}+3x^{2}-11x + 6\div(x - 1)\) is \(2x^{2}+5x - 6\).

Answer:

\(2x^{2}+5x - 6\)