Download - 8.5: FACTORING AX 2 + BX + C where A=1
8.5: FACTORING AX2 + BX + C where A=1.
Factoring: A process used to break down any polynomial into monomials.
FACTORING: ax2 + bx + c Procedure:
1) Always look for the GCF of all the terms2) 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:
x2+5x+6?
FACTORING: To factor a quadratic trinomial with a coefficient of 1 in the x2, we must look at the b and c coefficients:
x2+5x+6 x2+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= bThus the factored form is: (x+2)(x+3)
YOU TRY IT:
Ex: What is the FACTORED form of:
x2+7x+10?
SOLUTION: To factor a quadratic trinomial with a coefficient of 1 in the x2, we must look at the b and c coefficients:
x2+7x+10 x2+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 = bThus the factored form is: (x+2)(x+5)
YOU TRY IT:
Ex: What is the FACTORED form of:
x2-11x+24?
SOLUTION: x2-11x+24 x2+bx+c b= -11 c = +24
Look at the factors of C but notice that b = -11c = +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 -3+-8 = -11= bThus the factored form is: (x-3)(x-8)
YOU TRY IT:
Ex: What is the FACTORED form of:
x2+2x-15?
FACTORING: X2+2x-15 x2+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= bThus the factored form is: (x-3)(x+5)
YOU TRY IT:
Ex: What is the FACTORED form of:
x2-2x-35?
FACTORING: X2-2x-35 x2+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= bThus the factored form is: (x+5)(x-7)
REAL-WORLD:
A rectangular skateboard park has an area of x2+15x+54.What are the possible dimensions of the park? Use factoring.
FACTORING: X2+15x+54 x2+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= bThus a possible dimension is:(x+6)(x+9)
VIDEOS:Factoring
Quadratics
Factoring:
http://www.khanacademy.org/math/trigonometry/polynomial_and_rational/quad_factoring/v/factoring-quadratic-expressions
CLASSWORK:
Page 489-490:
Problems: As many as needed to master the concept