Factoring Polynomials by Synthetic Division

Front

What is synthetic division?

Back

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

Front

What is the first step in synthetic division?

Back

Write the coefficients of the polynomial in a row.

Front

In synthetic division, what do you do if a term is missing?

Back

You must place a zero as a coefficient for that term.

Front

What is the result of synthetic division called?

Back

The quotient and the remainder.

Front

How do you find the number to place in the left-hand box during synthetic division?

Back

It is the value of c from the binomial (x - c).

Front

What is the formula for factoring a difference of cubes?

Back

a³ - b³ = (a - b)(a² + ab + b²).

Front

What is the formula for factoring a sum of cubes?

Back

a³ + b³ = (a + b)(a² - ab + b²).

Front

How do you factor x³ + 27?

Back

x³ + 27 = (x + 3)(x² - 3x + 9).

Front

What is the significance of the remainder in synthetic division?

Back

The remainder indicates whether (x - c) is a factor of the polynomial; if the remainder is 0, it is a factor.

Front

What does it mean if a polynomial is prime?

Back

It cannot be factored into simpler polynomials with real coefficients.