Holt McDougal Algebra 1 7-3 Factoring x 2 + bx + c Example 1A: Factoring Trinomials by Guess and Check Factor x 2 + 15x + 36 by guess and check. (x + 3)(x + 12)
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Holt McDougal Algebra 1
7-3 Factoring x2
+ bx + c
Example 1A: Factoring Trinomials by Guess and
Check
Factor x2 + 15x + 36 by guess and check.
(x + 3)(x + 12)
Holt McDougal Algebra 1
7-3 Factoring x2
+ bx + c
Check It Out! Example 1a
Factor each trinomial by guess and check.
x2 + 10x + 24 (x + 4)(x + 6)
x2 + 7x + 12 (x + 3)(x + 4)
Holt McDougal Algebra 1
7-3 Factoring x2
+ bx + c
Holt McDougal Algebra 1
7-3 Factoring x2
+ bx + c
Example 2A: Factoring x2 + bx + c When c is Positive
x2 + 6x + 5
Factor each trinomial. Check your answer.
(x + 1)(x + 5)
x2 + 6x + 9 (x + 3)(x + 3)
x2 – 8x + 15 (x – 3)(x – 5)
x2 + 8x + 12 (x + 2)(x + 6)
Holt McDougal Algebra 1
7-3 Factoring x2
+ bx + c
You have solved quadratic equations by graphing. Another method used to solve quadratic equations is to factor and use the Zero Product Property.
Holt McDougal Algebra 1
7-3 Factoring x2
+ bx + c
Example 1A: Use the Zero Product Property
Use the Zero Product Property to solve the equation. Check your answer.
(x – 7)(x + 2) = 0
The solutions are {-2,7}
Plug in the sum of the
solutions
Holt McDougal Algebra 1
7-3 Factoring x2
+ bx + c
Example 1B: Use the Zero Product Property
Use the Zero Product Property to solve each equation. Check your answer.
(x – 2)(x) = 0
{0,2}
Plug in the product of the
solutions
Holt McDougal Algebra 1
7-3 Factoring x2
+ bx + c
Use the Zero Product Property to solve each equation. Check your answer.
Check It Out! Example 1a
(x)(x + 4) = 0
{-4,0}
Plug in the greater
solution
Holt McDougal Algebra 1
7-3 Factoring x2
+ bx + c
Check It Out! Example 1b
Use the Zero Product Property to solve the equation. Check your answer.
(x + 4)(x – 3) = 0
{-4,3}
Plug in lesser value
solution
Holt McDougal Algebra 1
7-3 Factoring x2
+ bx + c
Example 2A: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring. Check your answer.
x2 – 6x + 8 = 0
{2,4}
Plug in the sum of the
solutions
Holt McDougal Algebra 1
7-3 Factoring x2
+ bx + c
Example 2B: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring. Check your answer.
x2 + 4x = 21
{-7,3}
Plug in:
lesser value / greater
value
Holt McDougal Algebra 1
7-3 Factoring x2
+ bx + c
Example 2C: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring. Check your answer.
x2 – 12x + 36 = 0
{6}
Holt McDougal Algebra 1
7-3 Factoring x2
+ bx + c
Check It Out! Example 2a
Solve the quadratic equation by factoring. Check your answer.
x2 – 6x + 9 = 0
{3}
Holt McDougal Algebra 1
7-3 Factoring x2
+ bx + c
Check It Out! Example 2b
Solve the quadratic equation by factoring. Check your answer.
x2 + 4x = 5
{-5,1}
Plug in the product of the
solutions
Holt McDougal Algebra 1
7-3 Factoring x2
+ bx + c
Vertical Motion Model
A projectile is an object that is propelled into the air
but has no power to keep itself in the air. The height
of a projectile can be described by the vertical
motion model
The height h (in feet) of a projectile can be modeled
by
H = -16t2+vt+sWhere…
•t is the time (in seconds) the object has been in the
air
•v is the initial velocity (in feet per second)
•s is the initial height (in feet).
Holt McDougal Algebra 1
7-3 Factoring x2
+ bx + cExample 5ARMADILLO
A startled armadillo jumps straight into
the air with an initial vertical velocity of
14 feet per second. After how many
seconds does it land on the ground (as
a decimal)?h = –16t2 + vt + s
h = –16t2 + 14t
ANSWER
The armadillo lands on the ground 0.875 second after
the armadillo jumps.
Holt McDougal Algebra 1
7-3 Factoring x2
+ bx + c
Lesson Quiz: Part I
Use the Zero Product Property to solve each equation. Check your answers.
1. (x – 10)(x + 5) = 0
2. (x + 5)(x) = 0
Solve each quadratic equation by factoring. Check your answer.
3. x2 + 16x + 48 = 0
4. x2 – 11x = –24 •
{-5, 10}
{–5, 0}
{-12, –4}
{3, 8}
Holt McDougal Algebra 1
7-3 Factoring x2
+ bx + c
Lesson Quiz: Part I
Factor each trinomial.
1. x2 – 11x + 30
2. x2 + 10x + 9
3. x2 – 6x – 27
4. x2 + 14x – 32 (x + 16)(x – 2)
(x – 9)(x + 3)
(x + 1)(x + 9)
(x – 5)(x – 6)
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