Use synthetic division to find (x^2 - 7x + 12) ÷ (x - 4). Write your answer in the form q(x) + r/d(x), where q(x) is a polynomial, r is an integer, and d(x) is a linear polynomial. Simplify any fractions. ______

Set up synthetic division: Set up synthetic division with 4 as the root from x - 4 and the coefficients of x^2 - 7x + 12 as 1, -7, and 12.Perform synthetic division: Perform synthetic division: Bring down the leading coefficient (1). Multiply 4 by 1 and write the result (4) under -7. Add -7 and 4 to get -3. Multiply 4 by -3 and write the result (-12) under 12. Add 12 and -12 to get 0.Write the result: Write the result of synthetic division. The quotient is x - 3 and the remainder is 0.Express the result: Express the result as q(x) + r/d(x). Since the remainder is 0, the result is simply q(x), which is x - 3.

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Divide polynomials using synthetic division

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Q. Use synthetic division to find

(x^2 - 7x + 12) \div (x - 4)

\newline

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.

\newline

_________

Set up synthetic division: Set up synthetic division with $4$ as the root from $x - 4$ and the coefficients of $x^2 - 7x + 12$ as $1$ , $-7$ , and $12$ .
Perform synthetic division: Perform synthetic division: Bring down the leading coefficient $1$ . Multiply $4$ by $1$ and write the result $4$ under \$$-7$\). Add \$$-7$\) and $4$ to get \$$-3$\). Multiply $4$ by \$$-3$\) and write the result \$($-12$)\) under $12$. Add $12$ and \$$-12$\) to get $0$.
Write the result: Write the result of synthetic division. The quotient is $x - 3$ and the remainder is $0$.
Express the result: Express the result as $q(x) + \frac{r}{d(x)}$. Since the remainder is $0$, the result is simply $q(x)$, which is $x - 3$.