Use synthetic division to solve (x³ + 1) ÷ (x – 1). What is the quotient?
Answer: The quotient is x² + x + 1.
Mastering Synthetic Division
Synthetic division is a simplified method of dividing a polynomial by a binomial of the form (x – c). For (x³ + 1) ÷ (x – 1), set up the synthetic division and you’ll find the quotient is x² + x + 1. This technique is not only a shortcut for polynomial division but also an important algebraic skill. It simplifies computations, aids in finding polynomial roots, and is used in calculus for polynomial integration. Understanding this method enhances problem-solving efficiency and is a valuable tool in mathematics and related fields.
FAQ on Mastering Synthetic Division
How is synthetic division different from long division?
Synthetic division is a shortcut method specifically for dividing polynomials and is generally faster than long division.
When can synthetic division be used?
It can be used when dividing a polynomial by a binomial of the form (x – c).
What is the remainder when using synthetic division?
The remainder is the constant at the end of the synthetic division process.
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