Question

use synthetic division to find the result when $4x^4 - 7x^3 + 7x^2 - 12x + 15$ is divided by $x - 1$. if there is a remainder, express the result in the form $q(x) + \frac{r(x)}{b(x)}$.

Explanation:

synthetic division

$$\begin{array}{r|rrrrr} 1 & 4 & -7 & 7 & -12 & 15 \\ & & 4 & -3 & 4 & -8 \\ \hline & 4 & -3 & 4 & -8 & 7 \\ \end{array}$$

Step4: Form quotient and remainder

Quotient: $4x^3-3x^2+4x-8$, Remainder: $7$

Step5: Write final form

Result: $4x^3 - 3x^2 + 4x - 8 + \frac{7}{x-1}$

Answer:

synthetic division

$$\begin{array}{r|rrrrr} 1 & 4 & -7 & 7 & -12 & 15 \\ & & 4 & -3 & 4 & -8 \\ \hline & 4 & -3 & 4 & -8 & 7 \\ \end{array}$$

Step4: Form quotient and remainder

Quotient: $4x^3-3x^2+4x-8$, Remainder: $7$

Step5: Write final form

Result: $4x^3 - 3x^2 + 4x - 8 + \frac{7}{x-1}$