Synthetic Division Concepts and Applications

The video tutorial explains synthetic division as an alternative to long division for dividing polynomials by binomials in the form of X - K. It provides a detailed walkthrough of the process, including listing coefficients, using the opposite sign of the divisor's constant term, and performing calculations to find the quotient and remainder. Two examples are demonstrated: one with a remainder and one without, highlighting the differences and confirming the factorization of polynomials.

What is synthetic division primarily used for?

• Dividing a polynomial by a binomial in the form of x + k

• Dividing a polynomial by a binomial in the form of x - k

• Dividing a polynomial by another polynomial of the same degree

• Dividing a polynomial by a constant

What are the coefficients of the polynomial 1x^2 - 5x + 7?

• 1, -5, -7

• 1, -5, 7

• 1, 5, 7

• 1, 5, -7

In synthetic division, what operation is performed vertically?

• Division

• Addition

• Multiplication

• Subtraction

What is the remainder when dividing 1x^2 - 5x + 7 by x - 2 using synthetic division?

• 0

• 1

• -1

• 2

What is the quotient when dividing 1x^2 - 5x + 7 by x - 2?

• x - 2

• x + 2

• x - 3

• x + 3

What is the value of k when dividing by x + 2 in synthetic division?

• 1

• 2

• -2

• 0

What is the remainder when dividing 1x^2 + 8x + 12 by x + 2?

• 1

• -1

• 0

• 2

What is the quotient when dividing 1x^2 + 8x + 12 by x + 2?

• x + 2

• x - 6

• x - 2

• x + 6

What does a remainder of 0 indicate in synthetic division?

• The division process was incorrect

• The divisor is a factor of the dividend

• The divisor is not a factor of the dividend

• The quotient is incorrect

What is the degree of the quotient when dividing a degree 2 polynomial by a degree 1 binomial?

• 0

• 1

• 2

• 3