Factoring Polynomials and Expressions

The video tutorial covers various methods of factoring algebraic expressions, including the sum and difference of squares, using imaginary numbers, and factoring cubic and higher degree polynomials. It provides practice problems and explores special cases like the sum and difference of cubes, emphasizing the use of substitution and grouping techniques.

What is the factored form of x^2 - 4?

• (x + 1)(x - 1)

• (x + 2)(x - 2)

• (x + 2i)(x - 2i)

• (x + 4)(x - 4)

How can x^2 + 5 be factored using imaginary numbers?

• (x + √5)(x - √5)

• (x + 5i)(x - 5i)

• (x + 2.5)(x - 2.5)

• (x + i√5)(x - i√5)

What is the first step in factoring 3x^2 + 75?

• Apply the sum of cubes formula

• Extract the greatest common factor

• Use substitution

• Use the difference of squares formula

Which of the following is a factor of 5x^2 - 45?

• x - 3

• x + 3

• 5(x + 3)(x - 3)

• 5(x + 2)(x - 2)

What is the factored form of 2x^2 - 14?

• 2(x + √7)(x - √7)

• 2(x + 2√7)(x - 2√7)

• 2(x + 7)(x - 7)

• 2(x + 3.5)(x - 3.5)

How can the expression x^3 - x^2 + 16x - 16 be factored?

• (x - 1)(x^2 + 16)

• (x + 1)(x^2 - 16)

• (x - 1)(x^2 - 16)

• (x + 1)(x^2 + 16)

What substitution is used to factor x^4 - 5x^2 - 36?

• a = x^4

• a = x^3

• a = x

• a = x^2

Which formula is used to factor x^3 + 8?

• Difference of squares

• Sum of squares

• Sum of cubes

• Difference of cubes

What is the factored form of x^3 - 1?

• (x + 1)(x^2 + x + 1)

• (x - 1)(x^2 - x + 1)

• (x - 1)(x^2 + x + 1)

• (x + 1)(x^2 - x + 1)

What is the final factored form of the expression 3x^6 + 21x^3 - 24?

• 3(x + 2)(x - 1)(x^2 - 2x + 4)(x^2 + x + 1)

• 3(x + 1)(x - 2)(x^2 - x + 4)(x^2 + 2x + 1)

• 3(x + 1)(x - 2)(x^2 + x + 4)(x^2 - 2x + 1)

• 3(x + 2)(x - 1)(x^2 + 2x + 4)(x^2 - x + 1)