Questions: Find the quotient and remainder using long division. [ (x^2-4 x+7)/(x-3) ] quotient remainder

Transcript text: Find the quotient and remainder using long division. \[ \frac{x^{2}-4 x+7}{x-3} \] quotient $\square$ remainder $\square$

Solution

Step 1: Write down the coefficients of $P(x)$

The coefficients of $P(x)$ are [1, -4, 7] in descending order of their powers.

Step 2: Perform synthetic division

Using $a = 3$, perform synthetic division.

Step 3: Calculate the quotient and remainder

The quotient's coefficients are [1, -1] and the remainder is 4.

The quotient is $Q(x) = x^2 - x^1$ and the remainder is 4.

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