Questions: Use synthetic division to divide (7x^2+6x-7) by (x-1). Quotient: Remainder:

Transcript text: Use synthetic division to divide $\left(7 x^{2}+6 x-7\right)$ by $(x-1)$. Quotient: $\square$ Remainder: $\square$

Solution

Solution Steps

Step 1: Set up the Synthetic Division

Given the polynomial of degree $n = 2$ with coefficients [7, 6, -7] and divisor $x \pm 1$. We perform synthetic division by placing the constant $k = 1$ to the left and writing down the coefficients in descending order.

Step 2: Perform the Division

We bring down the leading coefficient as is and then multiply $k$ by the value just written down, placing the result under the next coefficient. We add the values in the current column and write the result beneath, continuing this process for all coefficients.

Step 3: Interpret the Result

The coefficients of the quotient polynomial $Q(x)$ are [7, 13], starting from $x^1$ down to $x^0$, and the last number, 6, represents the remainder.