HW 2.3 Synthetic Division

Front

What is synthetic division?

Back

A method used to divide a polynomial by a linear factor of the form (x - c) without using long division.

Front

In synthetic division, what does the left-hand box represent?

Back

The value of 'c' from the linear factor (x - c) being used for division.

Front

What is the first step in synthetic division?

Back

Write down the coefficients of the polynomial in descending order of degree.

Front

How do you handle missing terms in synthetic division?

Back

Use a zero as a placeholder for any missing coefficients.

Front

What is the significance of the remainder in synthetic division?

Back

The remainder represents the value of the polynomial at x = c, where c is the root of the divisor.

Front

If dividing (x^4 + 3x^2 - 4x - 2) by (x - 2), what mistake did Cam make?

Back

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

Front

What is the result of (2x^3 + 5x^2 + 9) ÷ (x + 3)?

Back

2x^2 - x + 3.

Front

How many zeros are needed in the top row for synthetic division of (x^6 + 4x^3 + 2)?

Back

4 zeros are needed for the missing x^5 and x^4 terms.

Front

What is the correct order of coefficients for (3x - 4x^3 + 6x^4 + 1) when divided by (x + 3)?

Back

6, -4, 0, 3, 1.

Front

What is the purpose of synthetic division?

Back

To simplify the process of dividing polynomials and finding roots.