Download Factoring Perfect Square Trinomials a2 + 2ab + b2 = (a + b)(a + b

Algebra
Date _________
Chapter 8 Quadratic Expressions and Equations
8-9 Perfect Squares
A.SSE.3a Factor a quadratic expression to reveal the zeros of the function it defines.
A.REI.1 Explain each step in solving a simple equation as following from the equality of
numbers asserted at the previous step, starting from the assumption that the original
equation has solution
Vocabulary
Perfect square trinomial –
Factoring Perfect Square Trinomials
a2 + 2ab + b2 = (a + b)(a + b) = (a + b)2
a2 – 2ab + b2 = (a – b)(a – b) = (a – b)2
Example: x 2 + 8x + 16 = (x + 4)(x + 4) or (x + 4)2
X2 – 6x + 9 = (x – 3)(x – 3) = (x – 3)2
Example 1 Recognize and Factor Perfect Square Trinomials
Determine whether each trinomial is a perfect square trinomial. Write yes or no. If so,
factor it.
a) 4y2 + 12y + 9
b) 9x2 – 6x + 4
Factoring Methods
Steps
Factor out the GCF
Check for a difference of squares
or a perfect square trinomial
Apply the factoring patterns for
x2+bx+c or ax2+bx+c or factor by
grouping
# of
terms
any
2 or 3
3 or 4
Examples
4x3 + 2x2 – 6x = 2x(2x2+x-3)
9x2-16=(3x+4)(3x-4)
16x2+24x+9 = (4x+3)2
X2-8x+12=(x – 2)(x _ 6)
2x2+13x+6 = (2x + 1)(x + 6)
2
12y + 9y + 8y + 6 = (12y2+9y)+(8y+6)
=3y(4y+3)+2(4y+3)
=(4y+3)(3y+2)
Example 2 Factor Completely
Factor each polynomial, if possible. If the polynomial cannot be factored write prime.
a) 5x2 – 80
b) 9x2 – 6x – 35
Example 3 Solve Equations with Repeated Factors
Solve 9x2 – 48x = -64
Square Root Property
To solve a quadratic equation in the form x2 = n, take the square root of each side
For any number n  0, if x2 = n, then x =  n
Example x2 = 25; x =  25 ; x =  5
Example 4 Use the Square Root Property
Solve each equation. Check your solutions.
a) (y – 6)2 = 81
b) (x + 6)2 = 12
Example 5 Solve an Equation
During an experiment, a ball is dropped from a height of 205 feet. The formula h = 16t2+h0 can be used to approximate the number of seconds t it takes for the ball to reach
height h from an initial height of h0 in feet. Find the time it takes the ball to reach the
ground.