Factoring Quadratics: GCF and Monics Explained

What is the standard form of a quadratic function?

• ax^2 + bx

• ax + b

• ax^2 + bx + c

• bx^2 + c

What does 'monic' mean in the context of quadratic expressions?

• There is no constant term

• The coefficient of x is one

• The coefficient of x^2 is zero

• The coefficient of x^2 is one

What is the purpose of factoring in algebra?

• To differentiate polynomials

• To simplify expressions into products of simpler expressions

• To solve quadratic equations

• To graph quadratic functions

Which method is used to multiply out two binomials?

• Substitution

• Division

• Factoring

• FOIL

What is the first step in factoring any polynomial?

• Apply the quadratic formula

• Divide by the leading coefficient

• Find the greatest common factor

• Sketch the graph

In the context of trinomials, what must the selected numbers multiply to?

• The variable x

• The constant term, c

• The coefficient of x, b

• The coefficient of x^2, a

How do you verify if your factoring of a trinomial is correct?

• By plotting the function

• By setting the equation to zero

• By checking if the discriminant is positive

• By re-foiling the factors

What does it mean if a quadratic expression is described as 'prime'?

• It can be factored into identical binomials

• It includes a prime number

• It cannot be factored into real number factors

• It has exactly two distinct factors

What is the significance of the 'a' value in the standard form of a quadratic expression?

• It determines if the quadratic is monic

• It affects the curvature of the parabola

• It is the y-intercept of the graph

• It represents the slope of the line

When factoring trinomials, what is the relationship between the numbers that multiply to 'c' and add to 'b'?

• They are the coefficients of the quadratic term

• They are the exponents in the factors

• They are the coefficients of the linear terms in the factors

• They represent the roots of the equation