Questions: Divide using synthetic division. (7 x^2+x-8) div(x-1) (7 x^2+x-8) div(x-1)= (Simplify your answer. Use integers or fractions for any numbers in the express

$Divide using synthetic division. (7 x^2+x-8) div(x-1) (7 x^2+x-8) div(x-1)= (Simplify your answer. Use integers or fractions for any numbers in the express$

Transcript text: Divide using synthetic division. \[ \begin{array}{c} \left(7 x^{2}+x-8\right) \div(x-1) \\ \left(7 x^{2}+x-8\right) \div(x-1)= \end{array} \] (Simplify your answer. Use integers or fractions for any numbers in the express

Solution

Solution Steps

Step 1: Set up the synthetic division

Given the polynomial $P(x)$ and the divisor $x - a$, we start by writing down the coefficient $a = 1$ and the coefficients of $P(x)$: [7, 1, -8].

Step 2: Perform the synthetic division

We bring down the leading coefficient as is and then proceed to multiply and add as per the synthetic division process. The coefficients of the quotient are obtained as follows: [7, 8].

Step 3: Determine the remainder

The remainder of the division is the last number obtained from the synthetic division process, which is 0.