Question

hw 13 dividing polynomials 5.4: problem 5 (2 points) use synthetic division to determine whether or not $(x - 4)$ is a factor of $(2x^{3}-11x^{2}+13x - 4)$. quotient: help (formulas) remainder: help (numbers) is $(x - 4)$ is a factor of $(2x^{3}-11x^{2}+13x - 4)$? yes no note: in order to get credit for this problem all answers must be correct. preview my answers submit answers show me another you have attempted this problem 0 times. you have 5 attempts left before new version will be requested. you have unlimited attempts remaining.

Explanation:

Step1: Set up synthetic division

For \(x - 4\), the zero is \(x = 4\). The polynomial \(2x^{3}-11x^{2}+13x - 4\) has coefficients \(2,-11,13,-4\).

4 |  2  -11  13  -4
   |     8  -12   4
   |----------------
     2   -3   1   0

Step2: Interpret the results

The numbers \(2,-3,1\) are the coefficients of the quotient polynomial. The degree of the original polynomial is \(3\), so the degree of the quotient is \(3 - 1=2\). The quotient is \(2x^{2}-3x + 1\) and the remainder is \(0\).

Answer:

Quotient: \(2x^{2}-3x + 1\)
Remainder: \(0\)
Is \((x - 4)\) a factor of \((2x^{3}-11x^{2}+13x - 4)\)? Yes