PERFECT SQUARE TRINOMIALS
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PERFECT SQUARE TRINOMIALS Any trinomial of the form ax 2 + bx + c that can be factored to be a (BINOMIAL Factor) squared Sum Factors : a 2 + 2ab + b 2 = (a + b) 2 Difference Factors : a 2 - 2ab + b 2 = (a - b) 2 (1) 9x 2 + 12x + 4 (2) x 2 - 8x + 16 (3) 4x 2 - 20x + 25 (4) x 2 + 20x + 100
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How do you make a perfect square trinomial? STEP 1: DIVIDE middle term value (b-value) by 2 STEP 2: SQUARE it STEP 3: Make your step 2 answer the constant FACTORS: Binomial is add if middle term is positive Binomial is subtract if middle term is negative EXAMPLE: x2 + 6x + c EXAMPLE: x2 - 10x + c Middle term: 6 Middle term: -10 Divide by 2: 3 Divide by 2: -5 Squared = 9 Squared = 25 x2 + 6x + 9 = (x + 3)2 x2 – 10x + 25 = (x - 5)2
Transcript of PERFECT SQUARE TRINOMIALS
PERFECT SQUARE TRINOMIALSAny trinomial of the form ax2 + bx + c that can be
factored to be a (BINOMIAL Factor) squaredSum Factors:
a2 + 2ab + b2 = (a + b)2 Difference Factors:
a2 - 2ab + b2 = (a - b)2
(1) 9x2 + 12x + 4 (2) x2 - 8x + 16
(3) 4x2 - 20x + 25 (4) x2 + 20x + 100
How do you make a perfect square trinomial?• STEP 1: DIVIDE middle term value (b-value) by 2• STEP 2: SQUARE it• STEP 3: Make your step 2 answer the constant
FACTORS: Binomial is add if middle term is positive
Binomial is subtract if middle term is negative
x2 + 6x + 9 = (x + 3)2
Middle term: 6Divide by 2: 3Squared = 9
EXAMPLE: x2 + 6x + c
x2 – 10x + 25 = (x - 5)2
Middle term: -10Divide by 2: -5Squared = 25
EXAMPLE: x2 - 10x + c
Create Perfect Square TrinomialsPractice finding “c”
• x2 - 8x + c
• x2 + 10x + c
• x2 - 3x + c
• x2 + 9x + c
Continued: Practice finding “c”
cxx 212cxx
652cxx
432
STEPS for COMPLETING THE SQUAREax2 + bx + c = 0
Step 1: Lead coefficient of x2 must be 1• DIVIDE by “a” value
Step 2: Subtract current ‘c’ term
Step 3: Find value to make a perfect square trinomial • Divide middle term, “bx”, by 2 and square• Add that value to both sides of equation
Step 4: Factor (perfect square!) *Shortcut = half of middle term is part of binomial factor*
Step 5: Solve for x
Example: Solve by completing the square• x2 + 6x + 4 = 0 - SUBTRACT 4
• x2 + 6x = - 4 - Find the constant value to create a perfect square and ADD to both sides
(half of 6 is 3, 3 squared is 9)
• x2 + 6x + 9 = -4 + 9 -FACTOR perfect square trinomial
• (x + 3)2 = 5 - SOLVE for x:Square root both sides Use plus or minus (Check to simplify radical)53
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x
x
Practice #1: Completing the Square01142 xx
04372 xx0252 xx
013122 xx1.
4.3.
2.
Example with leading coefficient0342 2 xx
2322 xx
02322 xx
- Divide every number by 2
- Add 3/2 on both sides
- Find c to make perfect square trinomial
(half of 2 = 1, 1 squares = 1
- Factor left side, combine like terms on the right
123122 xx
25)1( 2 x - Solve for x:
Square Root with plus/minus
Rationalize Fraction Radicals
Practice #2: Completing the Square1. 03112 2 xx
4. 3.
2.
02125 2 xx
0493 2 xx
0182 2 xx
Practice: Equations with Complex Solutions1. 0842 xx
4. 3.
2. 0342 2 xx
01062 xx 0564 2 xx
Practice : Solve Equations to equal zero?1. 2. 53342 2 xxx6842 xx
4. 3. xxx 2282 xxx 91732 2
