Factoring Polynomials: Key Concepts and Techniques

This video tutorial by Steve reviews various methods of factoring polynomials. It covers factoring by the greatest common factor (GCF), factoring polynomials of the form x² + bx + c, and using the AC method for ax² + bx + c. Special cases such as perfect square trinomials and the difference of squares are also discussed. The video concludes with a checklist for factoring and encourages students to reach out for further assistance.

What does GCF stand for?

• Greatest Calculated Figure

• Greatest Common Factor

• General Calculus Function

• Geometric Calculation Formula

What is the greatest common factor of 15x^2 and 10x?

• x

• 15x

• 10x

• 5x

To factor a polynomial in the form x^2 + bx + c, what must you find?

• Two numbers whose product is b and sum is c

• Two numbers whose sum is b and product is c

• Two numbers whose difference is b and sum is c

• Two numbers whose sum is b and difference is c

What are the factors of x^2 + 5x + 6?

• (x - 3) * (x + 2)

• (x + 3) * (x - 2)

• (x + 3) * (x + 2)

• (x - 3) * (x - 2)

What is the first step in the AC method of factoring?

• Find integers with a sum of b and a product of a*c

• Rewrite the middle term using the factors

• Factor out the GCF from each pair

• Rewrite the factors

What does the AC method help to factor?

• Difference of squares

• Polynomials in the form x^2 + bx + c

• Polynomials in the form ax^2 + bx + c

• Perfect square trinomials

What form does a perfect square trinomial take?

• a^2 - 2ab + b^2

• a^2 + ab + b^2

• a^2 + 2ab + b^2

• a^2 - ab + b^2

What is the factored form of a difference of squares?

• (a - b) * (a - b)

• (a + b) * (a - b)

• (a + b) * (a + b)

• a + b * a - b

What is the first question on the factoring checklist?

• Is the polynomial a perfect square?

• Can the polynomial be rewritten?

• What form is the polynomial in?

• Is there a GCF to factor out?

How do you check if your factoring is correct?

• By dividing

• By subtracting

• By multiplying

• By adding