Trinomial Factoring with lead coefficient of one Trinomials

Trinomial Factoring with lead coefficient of one Trinomials in the form: x 2 + bx + c FOIL: Notes:

Factoring is the opposite of FOIL Ex 1. x 2 + 7 x + 10 ( ) What must be the first term in each factor? The last terms has to have a product of 10, but a sum of 7. What can the last terms be?

Try some with all positive signs. b and c are positive x 2 + 3 x + 2 x 2+14 x+40 x 2 + 7 x +12

Try some where the second term is negative and the third term is positive b is negative and c is positive x 2 - 5 x + 6 The sum must be negative The product must be positive What does that mean about the numbers you select? Both numbers will be negative

x 2 - 9 x + 20 x 2 - 17 x + 30 x 2 -10 x + 16

Factoring when b is positive and c is negative x 2 +7 x -18 The sum must be positive The product must be negative What does that mean about the numbers yo select? One number is positive and one number is negative

x 2 + 5 x - 14 x 2 + 10 x - 200 x 2 +11 x - 26

Factoring when b and c are negative x 2 - 2 x - 8 The sum must be negative The product must be negative What does that mean about the numbers select? One number is negative and one is positive

Using the Discriminant to determine if the trinomial is factorable b 2 4 ac if the discriminant is a perfect square it is factorable if the discriminant is not a perfect square it is not factorable Use the discriminant to tell if the trinomial is factorable. If it is factorable, write the factorization 1. ) x 2 + 3 x 4 2. ) x 2 + 3 x 6

Solve the quadratic equations. ex 1: x 2 - 8 x + 15 = 0 Steps: 1). Eq. in standard form 2). discriminant: a). perfect sq. - factor b). not a perfect sq. quadratic formula 3). zero product property 4). Solve

ex 2: x 2 + 4 x = 21 ex 3: x 2 - 9 x + 12= 0

4. ) x 2 + 5 xy -14 y