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8.5: FACTORING AX 2 + BX + C where A=1.

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Factoring: A process used to break down any polynomial into monomials . 8.5: FACTORING AX 2 + BX + C where A=1. Procedure:. 1) Always look for the GCF of all the terms. FACTORING: ax 2 + bx + c . - PowerPoint PPT Presentation
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8.5: FACTORING AX 2 + BX + C where A=1. Factoring: A process used to break down any polynomial into monomials.
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Page 1: 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.

Page 2: 8.5: FACTORING AX 2  + BX +  C where A=1.

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.

Page 3: 8.5: FACTORING AX 2  + BX +  C where A=1.

GOAL:

Page 4: 8.5: FACTORING AX 2  + BX +  C where A=1.

FACTORING:

Ex: What is the FACTORED form of:

x2+5x+6?

Page 5: 8.5: FACTORING AX 2  + BX +  C where A=1.

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)

Page 6: 8.5: FACTORING AX 2  + BX +  C where A=1.

YOU TRY IT:

Ex: What is the FACTORED form of:

x2+7x+10?

Page 7: 8.5: FACTORING AX 2  + BX +  C where A=1.

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)

Page 8: 8.5: FACTORING AX 2  + BX +  C where A=1.

YOU TRY IT:

Ex: What is the FACTORED form of:

x2-11x+24?

Page 9: 8.5: FACTORING AX 2  + BX +  C where A=1.

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)

Page 10: 8.5: FACTORING AX 2  + BX +  C where A=1.

YOU TRY IT:

Ex: What is the FACTORED form of:

x2+2x-15?

Page 11: 8.5: FACTORING AX 2  + BX +  C where A=1.

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)

Page 12: 8.5: FACTORING AX 2  + BX +  C where A=1.

YOU TRY IT:

Ex: What is the FACTORED form of:

x2-2x-35?

Page 13: 8.5: FACTORING AX 2  + BX +  C where A=1.

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)

Page 14: 8.5: FACTORING AX 2  + BX +  C where A=1.

REAL-WORLD:

A rectangular skateboard park has an area of x2+15x+54.What are the possible dimensions of the park? Use factoring.

Page 15: 8.5: FACTORING AX 2  + BX +  C where A=1.

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)

Page 17: 8.5: FACTORING AX 2  + BX +  C where A=1.

CLASSWORK:

Page 489-490:

Problems: As many as needed to master the concept


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