Exploring Adding and Subtracting Rational Expressions

The video tutorial explains synthetic division, a shortcut method for dividing polynomials, focusing on coefficients. It provides multiple examples, highlighting the importance of dividing by the zero of the factor, not the factor itself. The tutorial compares synthetic division with long division, demonstrating the efficiency of the former. It also addresses handling missing powers in polynomials.

What is synthetic division primarily used for?

• Dividing polynomials by binomials with any coefficient

• Dividing polynomials by binomials with a coefficient of 1

• Dividing binomials by polynomials

• Dividing any two algebraic expressions

In synthetic division, what do you divide by?

• The constant term

• The factor

• The coefficient

• The zero

What is the first step in synthetic division?

• Drop down the first coefficient

• Divide the coefficients

• Multiply the coefficients

• Add the coefficients

In the example with 2n^2 - 16n + 19, what is the remainder?

• 19

• 14

• 5

• 2

When dividing y^3 + 5y^2 - 7y + 2 by y - 2, what is the zero?

• -7

• 2

• -2

• 7

What is the remainder when dividing y^3 + 5y^2 - 7y + 2 by y - 2?

• 2

• 16

• 14

• 7

How do you handle missing powers in synthetic division?

• Skip the division

• Use one as the coefficient for the missing power

• Use zero as the coefficient for the missing power

• Ignore the missing power

What is the remainder when dividing k^3 - 17k + 32 by k + 5?

• 32

• 8

• -32

• -8

In long division, what do you do after distributing the first term?

• Drop down the next term

• Add the coefficients

• Change the signs and subtract

• Multiply the coefficients

What is the quotient when dividing n^3 - 3n^2 - 11n - 3 by n + 1 using synthetic division?

• n^2 + 4n - 7 + 4/(n+1)

• n^2 - 4n + 7 + 4/(n+1)

• n^2 + 4n + 7 + 4/(n+1)

• n^2 - 4n - 7 + 4/(n+1)