Math 3 Factoring & Quadratic Formula Review

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does it mean if the discriminant (b² - 4ac) is negative?

Back

If the discriminant is negative, the quadratic equation has no real solutions, meaning the graph does not intersect the x-axis.

Front

How do you factor a quadratic expression?

Back

To factor a quadratic expression, look for two numbers that multiply to 'c' (the constant term) and add to 'b' (the coefficient of x).

Front

What is the first step in factoring a polynomial?

Back

The first step in factoring a polynomial is to look for the Greatest Common Factor (GCF) of all the terms.

Front

What is the difference of squares?

Back

The difference of squares is a factoring technique used for expressions in the form a² - b², which can be factored as (a - b)(a + b).

Front

Can you factor 49x² + 4y²? Why or why not?

Back

No, you cannot factor 49x² + 4y² using the difference of squares because it is an addition, not a subtraction.

Front

What is the factored form of 32n² - 50?

Back

The factored form is 2(4n + 5)(4n - 5).

Front

How do you solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, set the equation to zero, factor the quadratic, and then set each factor equal to zero to find the solutions.

Front

What are the solutions of the equation x² + 8x + 15 = 0?

Back

The solutions are x = -3 and x = -5.

Front

What is the significance of the GCF in factoring?

Back

The GCF helps simplify the polynomial before further factoring, making the process easier.