Lesson 6: 8-6 Factoring Quadratic Trinomials

When a is 1, how can you check to see if you chose the correct pair of factors?
When the last term is positive but the coefficient of the middle term is negative, what are the signs of the two factors?
When the last term is negative, how can you check to see if you chose the right factors?
When a is not 1, how do we start to look for factor pairs?
What does it mean for a trinomial to be prime?
How can you check to see if your factorization is correct?

prime polynomial

A.SSE.2 Use the structure of an expression to identify ways to rewrite it.

SAT questions related to multiplying binomials: 4-3-5, 6-3-15, 4-4-28, 5-4-35, 8-3-5, 1-3-15; factoring: 5-3-4, 3-3-7

A trinomial of the form ax^2+bx+c may or may not be factorable into binomial factors. If the trinomial is factorable, then the factors of ac must be two integers m and p such that m+p=b and mp=ac. When a =1, the trinomials is in the form x^2+bx+c and the factors of c must be two integers, m and p, such that m+p=b and mp=c.

Diana is having a rectangular hot tub installed near her pool. A 24-foot fence is to surround the hot tub. If the hot tub will cover an area of 36 square feet, what will be the dimensions of the hot tub?
To solve this problem, the landscape architect needs to find two numbers that have a product of 36 and a sum of 12, half the perimeter of the hot tub.

Students may need to be reminded that the order in which they record the factors does not matter. So, (x+m)(x+p) and (x+p)(x+m) are both correct.

If some students have trouble factoring polynomials, then place students in groups to factor polynomials. Depending on the number of factors and number of students in each group, have each student find one or two factors of mp. By dividing the labor, students should be able to find the factors for mp that sum to m+p quickly. Once they have found the factors, have students complete the factoring as a group.

Practice: Exercises 1 -10

Exercises 54-62

McGraw Hill resources