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 than long division and focuses on the coefficients of the polynomial.

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How do you set up synthetic division?

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To set up synthetic division, write the coefficients of the polynomial in descending order. If any degree is missing, use a zero as a placeholder. Place the value of c (from x - c) to the left.

Front

What is the purpose of using a zero placeholder in synthetic division?

Back

A zero placeholder is used to maintain the correct degree of the polynomial when a term is missing. It ensures that the synthetic division process accurately reflects the polynomial's structure.

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What is the result of dividing (x^3 - 3x^2 - 10x + 24) by (x + 3)?

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The result is (x - 4)(x - 2).

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What are the coefficients obtained after performing synthetic division on (3x - 4x^3 + 6x^4 + 1) by (x + 3)?

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The coefficients are 6, -4, 0, 3, 1.

Front

What mistake did Cam make when dividing (x^4 + 3x^2 - 4x - 2) by (x - 2)?

Back

Cam did not use a zero placeholder for the x^3 term.

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What is the result of dividing (4x^4 + 4x^3 - 9x^2 - x + 2) by (x - 1)?

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The result is 4x^3 + 8x^2 - x - 2.

Front

When dividing a polynomial by (x - 1), what number should be used in synthetic division?

Back

The number to use is 1.

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What is the remainder in synthetic division?

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The remainder is the last value obtained after performing synthetic division, representing what is left over after the division.

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How do you factor a polynomial after synthetic division?

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After synthetic division, the quotient can be factored further if it is a polynomial of degree 2 or higher, often using methods like factoring by grouping or applying the quadratic formula.