use synthetic division to find the result when $3x^{3}-17x^{2}+13x + 23$ is divided by $x - 4$. if there is…

use synthetic division to find the result when $3x^{3}-17x^{2}+13x + 23$ is divided by $x - 4$. if there is a remainder, express the result in the form $q(x)+\frac{r(x)}{b(x)}$.

use synthetic division to find the result when $3x^{3}-17x^{2}+13x + 23$ is divided by $x - 4$. if there is a remainder, express the result in the form $q(x)+\frac{r(x)}{b(x)}$.

Answer

Explanation:

Step1: Set up synthetic division

Write 4 (from (x - 4)) on the left. List the coefficients 3, - 17, 13, 23 of (3x^{3}-17x^{2}+13x + 23).

Step2: Bring down the first coefficient

Bring down the first coefficient 3.

Step3: Multiply and add

Multiply 4 by 3 to get 12. Add - 17 and 12 to get - 5.

Step4: Multiply and add again

Multiply 4 by - 5 to get - 20. Add 13 and - 20 to get - 7.

Step5: Multiply and add one - more time

Multiply 4 by - 7 to get - 28. Add 23 and - 28 to get - 5. The numbers 3, - 5, - 7 are the coefficients of the quotient polynomial (q(x)) and - 5 is the remainder (r(x)), and (b(x)=x - 4). The quotient polynomial (q(x)=3x^{2}-5x - 7).

Answer:

(3x^{2}-5x - 7+\frac{-5}{x - 4})