FACTORING RULES. *GCF( Greatest Common Factor) – First Rule 4 TERMS Grouping 3 TERMS Perfect Square Trinomial AC Method with Grouping 2 TERMS Difference Of Two Squares Sum or Difference Of Two Cubes.
Perfect Square Trinomial
AC Method with Grouping
Difference Of Two Squares
Sum or Difference Of Two Cubes
We will explore factoring trinomials using the ac method with grouping next and come back to Perfect Square Trinomials later.
The first rule of factoring is to factor out the Greatest Common Factor(GCF).
Stop! Check that you have factored the (GCF)correctly by distributing it back through the remaining polynomial to obtain the original trinomial.
After factoring out the (GCF), the remaining polynomial is of the form
To factor , we must find two integers whose product is ac and whose sum is b.
To factor , we must find two integers whose product is -60 and whose sum is 7.
SUM OF FACTORS OF
ac = b = 7
Replace b = 7 in our original expression with
b = 12 + (-5).
Factoring is an algebraic process which allows us to solve quadratic equations pertaining to real-world applications, such as remodeling a kitchen or building a skyscraper.
We will cover the concept of solving quadratic equations and then investigate some real-world applications.
A quadratic equation is an equation that can be written in standard form
where a, b, and c represent real numbers, and
using factoring and the
When the product of two real numbers is 0, at least one of them is 0.
If a and b represent real numbers, and
if then a=0 or b=0
The height h in feet reached by a dolphin t seconds after
breaking the surface of the water is given by h
How long will it take the dolphin to jump out of the water and touch the trainer’s hand?
From the top of the building a ball is thrown straight up with an initial velocity of 32 feet per second. The equation below gives the height s of the ball t seconds after thrown. Find the maximum height reached by the ball and the time it takes for the ball to hit the ground.