Exploring Synthetic Division in Algebra 2

The video tutorial introduces synthetic division as a faster alternative to long division for polynomials. It explains the process of synthetic division, including changing the sign of the divisor and working with coefficients. The tutorial provides step-by-step instructions and examples to illustrate the method. It also covers the remainder theorem and its application in synthetic division, emphasizing the efficiency and reduced error potential of this method.

What is one advantage of synthetic division over long division?

• It is more accurate.

• It is faster.

• It uses more variables.

• It is easier to understand.

What must you remember to do with the divisor in synthetic division?

• Double it.

• Divide it by 2.

• Square it.

• Change its sign.

In synthetic division, what do you do after bringing down the first number?

• Multiply and add.

• Subtract and divide.

• Add and subtract.

• Divide and multiply.

If the highest degree of the polynomial is 3, what will be the degree of the first term in the quotient?

• 2

• 3

• 0

• 1

What is the remainder when the polynomial x^3 + 4x^2 + x - 6 is divided by x + 1 using synthetic division?

• -6

• 0

• 4

• -4

What should you do if a term is missing in the polynomial during synthetic division?

• Subtract a zero for the missing term.

• Add a one for the missing term.

• Add a zero for the missing term.

• Ignore it.

What is the final quotient when x^2 - 4x + 3 is factored completely?

• (x + 3)(x + 1)

• (x - 3)(x + 1)

• (x + 3)(x - 1)

• (x - 3)(x - 1)

When can you factor a polynomial completely using synthetic division?

• When the remainder is zero.

• When the remainder is one.

• When the remainder is negative.

• When the remainder is positive.

According to the remainder theorem, what is the remainder when a polynomial is divided by x - a?

• The value of the polynomial at x = 1.

• The value of the polynomial at x = a.

• The value of the polynomial at x = -a.

• The value of the polynomial at x = 0.

What is the remainder when the polynomial 2x^4 + 6x^3 - 5x^2 - 60 is divided by x + 1 using synthetic division?

• -69

• 69

• 9

• -9