Question

use synthetic division to find $(7x^{3}-20x^{2}-28x - 5)div(x - 4)$. write your answer in the form $q(x)+\frac{r}{d(x)}$, where $q(x)$ is a polynomial, $r$ is an integer, and $d(x)$ is a linear polynomial. simplify any fractions.

Explanation:

Step1: Set up synthetic division

Root: $4$; Coefficients: $7, -20, -28, -5$

Step2: Bring down leading coefficient

$7$

Step3: Multiply and add for next term

$4×7=28$; $-20+28=8$

Step4: Repeat multiplication and addition

$4×8=32$; $-28+32=4$

Step5: Repeat again for remainder

$4×4=16$; $-5+16=11$

Step6: Form quotient and remainder

Quotient: $7x^2 + 8x + 4$; Remainder: $11$

Step7: Write final form

$7x^2 + 8x + 4 + \frac{11}{x - 4}$

Answer:

$7x^2 + 8x + 4 + \frac{11}{x - 4}$