Understanding Remainders and Synthetic Division

The video tutorial introduces synthetic division, a method for dividing polynomials, by first revisiting basic division concepts such as quotient, remainder, and divisor. It then explains synthetic division using polynomial examples, demonstrating the process step-by-step. The tutorial includes multiple examples, each with increasing complexity, to illustrate how synthetic division simplifies polynomial division. The video concludes with a complex example involving a coefficient in the divisor, emphasizing the method's efficiency and accuracy.

What is the term for the number that is left over after division?

• Quotient

• Divisor

• Remainder

• Dividend

In basic division, what do you call the number you divide by?

• Remainder

• Divisor

• Quotient

• Dividend

What is the result of dividing 7164 by 5?

• 1430 with a remainder of 2

• 1430 with a remainder of 4

• 1432 with a remainder of 4

• 1432 with a remainder of 2

What is the first step in synthetic division?

• Set the divisor equal to zero

• Draw the L shape

• Write down the coefficients

• Evaluate the nested form

When using synthetic division, what do you write to the left of the vertical line?

• The solution to the divisor set to zero

• The remainder

• The original polynomial

• The divisor

What is the degree of the quotient in synthetic division compared to the original polynomial?

• The same

• Two less

• One less

• One more

In synthetic division, what do the numbers at the bottom represent?

• The original polynomial

• The divisor

• The coefficients of the quotient

• The remainder

What is the remainder when dividing f(x) = 4x^3 + 7x^2 + 2 by x + 2 using synthetic division?

• -49

• 2

• 3

• 0

How do you express a polynomial in the form f(x) = (x - h)Q(x) + r?

• By using the quotient and remainder

• By using the original polynomial

• By using the divisor and quotient

• By using the divisor and remainder

What is the remainder when dividing f(x) = 4x^4 + 3x^3 - 6x^2 + 3 by 2x - 1?

• 0

• 3

• 2

• 1