Factoring Polynomials Techniques

Miss Morin introduces various factoring methods, including factoring the greatest common factor, using the X method for trinomials, and factoring by grouping. She provides examples and tips for each method, emphasizing the importance of checking work and choosing the most efficient method. The video covers both basic and advanced techniques, helping students become proficient in factoring.

What is the first step in choosing a factoring method?

• Use the quadratic formula

• Check if the polynomial is prime

• Look for a common monomial to factor out

• Apply the difference of squares

When factoring x^2 - 1, what is the result?

• x^2 + 1

• (x - 1)(x - 1)

• (x + 1)(x - 1)

• (x + 1)(x + 1)

In the diamond method, what do you need to find?

• Two numbers that multiply to the constant term and add to the leading coefficient

• Two numbers that multiply to the linear coefficient and add to the constant term

• Two numbers that multiply to the constant term and add to the linear coefficient

• Two numbers that multiply to the leading coefficient and add to the constant term

What is the purpose of factoring by grouping?

• To apply the quadratic formula

• To simplify polynomials with no common factor

• To solve linear equations

• To find the roots of a polynomial

How can you simplify a polynomial before using other factoring methods?

• Apply the difference of squares

• Factor out any common factors first

• Check if the polynomial is prime

• Use the quadratic formula

What should you do if a polynomial has no common factor?

• Use the grouping method

• Apply the quadratic formula

• Use the difference of squares

• Check if the polynomial is prime

When factoring higher degree polynomials, what should you identify first?

• The roots of the polynomial

• The greatest common factor

• The constant term

• The leading coefficient

What is a key characteristic of a difference of squares?

• It must have a negative sign between the terms

• It must have a positive sign between the terms

• It must have equal coefficients

• It must have a leading coefficient of one

What is the final step in ensuring a polynomial is completely factored?

• Use the difference of squares

• Apply the quadratic formula

• Check that no further factoring is possible

• Verify the polynomial is prime