Polynomial Division and Factoring Concepts

The video tutorial covers solving algebraic expressions using two methods: plugging in numbers and long division. It begins with problem 69, where the expression is evaluated by substituting values and then confirmed using long division. The tutorial then introduces problem 70, focusing on factoring and simplifying the expression before verifying the solution with long division. The video emphasizes understanding both methods to solve algebraic problems effectively.

What is the result of substituting x = 2 into the expression 12x^2 - 8x + 15 divided by 2x - 3?

• 47

• 8

• 7

• 12

Which answer choice was found to be equivalent to the expression after substitution?

• Choice D

• Choice A

• Choice B

• Choice C

What is the first step in the long division process for polynomials?

• Add

• Divide

• Subtract

• Multiply

What is the remainder when 12x^2 - 8x + 15 is divided by 2x - 3 using long division?

• 15

• 30

• 0

• 47

What is the first step in solving the new polynomial division problem involving r(x) and s(x)?

• Factor the numerator

• Simplify the denominator

• Substitute values

• Use long division

Which method is used to factor the expression x^2 - 9?

• Quadratic formula

• Synthetic division

• Completing the square

• Difference of squares

What are the factors of the expression x^2 - 9?

• (x + 3)(x - 3)

• (x + 5)(x - 5)

• (x + 9)(x - 9)

• (x + 1)(x - 1)

What is the simplified form of the expression after canceling common factors?

• 2x - 3

• 2x - 7

• x - 5

• x + 3

What is the final quotient when 2x^2 - 13x + 21 is divided by x - 5?

• 2x + 3 - 6/(x - 5)

• 2x - 3 - 6/(x - 5)

• 2x + 3 + 6/(x - 5)

• 2x - 3 + 6/(x - 5)

Which answer choice corresponds to the final solution of the polynomial division problem?

• Choice A

• Choice D

• Choice B

• Choice C