8.5: FACTORING AX 2 + BX + C where A=1. Factoring: A process used to break down any polynomial into monomials.

FACTORING: ax 2 + bx + c Procedure: 1) Always look for the GCF of all the terms 2) Factor the remaining terms – pay close attention to the value of coefficient a and follow the proper steps. 3) Re-write the original polynomial as a product of the polynomials that cannot be factored any further.

GOAL:

FACTORING: Ex: What is the FACTORED form of: x 2 +5x+6?

FACTORING: To factor a quadratic trinomial with a coefficient of 1 in the x 2, we must look at the b and c coefficients: x 2 +5x+6 x 2 +bx+c  b= +5  c = +6 Look at the factors of C:  c = +6 : (1)(6), (2)(3) Take the pair that equals to b when adding the two integers. In our case it is 2x3 since 2+3 = 5= b Thus the factored form is: (x+2)(x+3)

YOU TRY IT: Ex: What is the FACTORED form of: x 2 +7x+10?

SOLUTION: To factor a quadratic trinomial with a coefficient of 1 in the x 2, we must look at the b and c coefficients: x 2 +7x+10 x 2 +bx+c  b= +7  c = +10 Look at the factors of C:  c = +10 : (1)(10), (2)(5) Take the pair that equals to b when adding the two integers. In our case it is 2x5 since 2+5 = 7 = b Thus the factored form is: (x+2)(x+5)

YOU TRY IT: Ex: What is the FACTORED form of: x 2 -11x+24?

SOLUTION: x 2 -11x+24 x 2 +bx+c  b= -11  c = +24 Look at the factors of C but notice that b = -11  c = +24 : (-1)(-24), (-2)(-12), (-3)(-8), (-4)(-6) Take the pair that equals b when adding the two integers. In this case: (-3)(-8) since = -11= b Thus the factored form is: (x-3)(x-8)

YOU TRY IT: Ex: What is the FACTORED form of: x 2 +2x-15?

FACTORING: X 2 +2x-15 x 2 +bx+c  b= +2  c = -15 Look at the factors of C:  c = -15 : (-1)(15), (1)(-15), (-3)(5), (3)(-5) Take the pair that equals b when adding the two integers. In this case: (-3)(5) since -3+5 = +2= b Thus the factored form is: (x-3)(x+5)

YOU TRY IT: Ex: What is the FACTORED form of: x 2 -2x-35?

FACTORING: X 2 -2x-35 x 2 +bx+c  b= -2  c = -35 Look at the factors of C:  c = -35 : (-1)(35), (1)(-35), (-5)(7), (5)(-7) Take the pair that equals b when adding the two integers. In this case: (5)(-7) since 5+-7 = -2= b Thus the factored form is: (x+5)(x-7)

REAL-WORLD: A rectangular skateboard park has an area of x 2 +15x+54. What are the possible dimensions of the park? Use factoring.

FACTORING: X 2 +15x+54 x 2 +bx+c  b= +15  c =+54 Look at the factors of C:  c = +54 : (1)(54), (2)(27), (6)(9) Take the pair that equals b when adding the two integers. In this case: (6)(9) since 6+9 = 15= b Thus a possible dimension is:(x+6)(x+9)

VIDEOS: Factoring Quadratics Factoring: omial_and_rational/quad_factoring/v/factoring- quadratic-expressions

CLASSWORK: Page : Problems: As many as needed to master the concept