Synthetic Division

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear divisor of the form (x - c). It is faster and more efficient than long division for polynomials.

Front

What is the first step in synthetic division?

Back

The first step in synthetic division is to set up the synthetic division by writing down the coefficients of the polynomial and the value of c from the divisor (x - c).

Front

How do you handle coefficients of zero in synthetic division?

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If there are missing degrees in the polynomial, you represent their coefficients as zero when setting up synthetic division.

Front

What is the result of synthetic division?

Back

The result of synthetic division is a quotient polynomial and a remainder. The quotient is of one degree less than the original polynomial.

Front

How do you interpret the remainder in synthetic division?

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The remainder in synthetic division can be expressed as a fraction over the divisor. For example, if the remainder is r and the divisor is (x - c), it is expressed as r/(x - c).

Front

What is the relationship between synthetic division and the Remainder Theorem?

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The Remainder Theorem states that the remainder of the division of a polynomial f(x) by (x - c) is equal to f(c). Synthetic division provides a way to find this remainder efficiently.

Front

What is the significance of the coefficients in synthetic division?

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The coefficients of the polynomial are used in synthetic division to perform the calculations, and they determine the terms of the resulting quotient polynomial.

Front

How do you perform synthetic division for (2x^3 + 5x^2 + 9) ÷ (x + 3)?

Back

Set up synthetic division with coefficients [2, 5, 0, 9] and use -3 (from x + 3) as the divisor. Perform the synthetic division steps to find the quotient 2x^2 - x + 3.

Front

What is the quotient when dividing (3x^3 + 5x - 1) by (x + 1)?

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The quotient is 3x^2 - 3x + 8 with a remainder of -9, expressed as -9/(x + 1).

Front

How do you express the final answer of synthetic division?

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The final answer of synthetic division is expressed as the quotient polynomial plus the remainder divided by the divisor.