Finding Zeroes and GCF of Polynomials

This video tutorial teaches how to find the zeros of quadratic functions by factoring out the greatest common factor (GCF). It explains the concept of GCF, demonstrates the process of factoring polynomials, and addresses common misconceptions. The tutorial provides step-by-step examples to find zeros using the zero product property and checks solutions for accuracy. Key points include understanding the role of GCF in factoring and recognizing that if the GCF contains a variable, one zero will be zero.

What is the greatest common factor (GCF) of a polynomial?

• The smallest monomial that divides the polynomial

• The largest monomial that is a factor of the polynomial

• The sum of all coefficients in the polynomial

• The product of all terms in the polynomial

What is the GCF of the polynomial 20x^2 + 12x?

• 2x

• 6x

• 4x

• 8x

When factoring 20x^2 + 12x, what is the first term in the second factor?

• 3

• 5x

• 4x

• 2x

Why might someone mistakenly think x^2 + 9x cannot be factored?

• Because it is a sum of two squares

• Because it is a difference of squares

• Because it is already in factored form

• Because it has no constant term

What is the factored form of x^2 + 9x?

• x(x + 9)

• x(x - 9)

• (x - 3)(x + 3)

• (x + 3)(x + 3)

What are the zeroes of the function f(x) = 2x^2 + 4x?

• 2 and -2

• 0 and 2

• 0 and -2

• 1 and -1

What property is used to find the zeroes of a factored polynomial?

• Distributive Property

• Associative Property

• Zero Product Property

• Commutative Property

What is the significance of the GCF in finding zeroes of a function?

• It changes the degree of the polynomial

• It has no significance

• It simplifies the polynomial

• It always results in a zero of the function

What are the zeroes of the function f(x) = x^2 + 9x?

• 9 and -9

• 0 and 9

• 0 and -9

• 1 and -1

If a polynomial's GCF contains a variable, what can be inferred?

• The polynomial is linear

• One of the zeroes is 0

• The polynomial has no zeroes

• The polynomial is prime