Factoring Polynomials and Expressions

This video tutorial covers various methods for factoring polynomials, including using the greatest common factor (GCF), difference of perfect squares, sum and difference of cubes, and synthetic division. It also explores factoring trinomials with different coefficients, using substitution, and completing the square. The tutorial provides examples and explanations for each method, helping students understand how to apply these techniques to solve polynomial equations.

What is the first step in factoring the expression 7x + 21?

• Apply the quadratic formula

• Identify the difference of squares

• Find the greatest common factor

• Use synthetic division

How do you factor x^2 - 25?

• (x + 5)(x - 5)

• (x + 25)(x - 1)

• (x - 25)^2

• (x + 5)^2

When factoring a trinomial like x^2 + 11x + 30, what should you look for?

• Two numbers that multiply to 30 and add to 11

• Two numbers that multiply to 11 and subtract to 30

• Two numbers that multiply to 11 and add to 30

• Two numbers that multiply to 30 and subtract to 11

What is the method called when you replace a variable to simplify factoring?

• Synthetic division

• Substitution

• Completing the square

• Trial and error

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

• a^3 + b^3 = (a + b)(a^2 - ab + b^2)

• a^2 + b^2 = (a + b)(a - b)

• a^2 - b^2 = (a + b)(a - b)

• a^3 - b^3 = (a - b)(a^2 + ab + b^2)

What is the cube root of 27x^3?

• 27x

• 9x

• 3x

• x

In synthetic division, what do you do if the remainder is zero?

• The polynomial cannot be factored

• The divisor is a factor

• The divisor is not a factor

• The polynomial is prime

What is the result of factoring x^2 - 4 using the difference of squares?

• (x + 2)(x - 2)

• (x + 4)(x - 4)

• (x + 2)^2

• (x - 2)^2

How do you factor x^2 + 4 using imaginary numbers?

• (x + 4)(x - 4)

• (x + 2)(x - 2)

• (x + 4i)(x - 4i)

• (x + 2i)(x - 2i)

What is the first step in factoring a polynomial using synthetic division?

• Identify the GCF

• List possible factors

• Use the quadratic formula

• Complete the square