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Use synthetic division to find .Write your answer in the form , where is a polynomial, is an integer, and is a linear polynomial. Simplify any fractions._________
Full solution
Q. Use synthetic division to find .Write your answer in the form , where is a polynomial, is an integer, and is a linear polynomial. Simplify any fractions._________
- Set up synthetic division: Set up synthetic division with as the root from and the coefficients of as , , and .
- Perform synthetic division: Perform synthetic division: Bring down the leading coefficient . Multiply by and write the result 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 \(x - 3\).
