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INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith
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For more information, please see full course syllabus of Algebra 1
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Lecture Comments (4)

1 answer

Last reply by: Dr Carleen Eaton
Thu Oct 9, 2014 11:41 PM

Post by sadia sarwar on September 23, 2014

in example three does it mean that if we substitute both -1 and 13 the equasion would equal?

1 answer

Last reply by: Dr Carleen Eaton
Sat Jun 22, 2013 1:11 PM

Post by Taylor Wright on June 21, 2013

In example 3:

Could you also subtract 196 from both sides, giving you:

4x^2 - 48x - 52 = 0

4(x^2 - 12x -13) = 0

4(x^2 + 1x - 13x - 13) = 0

4(1x(x+1) - 13(x+1)) = 0

4(x+1)(x-13) = 0

x= -1 or 13

Factoring Perfect Squares

  • The special rules for factoring a perfect square trinomial are a2 + 2ab + b2 = (a + b)(a + b) and a2 - 2ab + b2 = (a - b)(a - b).
  • Learn to recognize perfect square trinomials in more complicated forms. This is an important skill you will need in later work in this course.
  • Some polynomials require several methods to be factored completely. Always start by finding the Greatest Common Factor. Then try other methods.
  • You can solve some quadratic equations by factoring the trinomial and then using the zero product property.
  • The square root property states that if x2 = n, then x = √n or x = -√n. You can use this property to solve some quadratic equations.

Factoring Perfect Squares

Factor:
64g2 − 80g + 25
( 8g − 5 )2
Factor:
121s2 + 154s + 49
( 11s + 7 )2
Factor:
81h2 − 180h + 100
( 9h − 10 )2
Factor:
20c3 − 60c + 45c
  • 5c( 4c2 − 12c + 9 )
5c( 2c − 3 )2
Factor:
50e3 − 120e2 + 72e
  • 2e( 25e2 − 60e + 36 )
2e( 5e − 6 )2
Factor:
192z3 + 576z2 + 432z
  • 3z( 64z2 + 192z + 144 )
3z( 8z + 12 )2
Solve:
2y2 − 16y + 32 = 50
  • 2( y2 − 8y + 16 ) = 50
  • 2( y − 4 )2 = 50
  • ( y − 4 )2 = 25
  • √{( y − 4 )2} = ±√{25} y − 4 = ±5 y − 4 = 5y = 9
  • y − 4 = − 5y = − 1
y{ − 1,9}
Solve:
3b2 + 150b + 75 = 147
  • 3( b2 + 50b + 25 ) = 147
  • 3( b + 5 )2 = 147
  • ( b + 5 )2 = 49
  • b + 5 = ±7
  • b + 5 = 7b = 2
  • b + 5 = − 7b = − 12
b = { − 12,2}
Solve:
16m2 − 48m + 36 = 256
  • 4(4m2 − 12m + 9) = 256
  • 4( 2m − 3 )2 = 256
  • ( 2m − 3 )2 = 64
  • 2m − 3 = ±8
  • 2m = ±11
  • 2m = 11m = [11/2]
  • 2m = − 11m = − [11/2]
m = { − [11/2],[11/2] }
Solve:
63a2 + 336a + 448 = 567
  • 7( 9a2 + 48a + 64 ) = 567
  • 7( 3a + 8 )2 = 567
  • ( 3a + 8 )2 = 81
  • 3a + 8 = ±9
  • 3a + 8 = 93a = 1a = [1/3]
  • 3a + 8 = − 93a = − 17a = − [17/3]
a = { − [17/3],[1/3] }

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Factoring Perfect Squares

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Perfect Squares 0:07
    • Example: Perfect Square Trinomials
  • Solving Equations 2:57
    • Square Root Property
    • Example
  • Example 1: Factor the Polynomial 5:09
  • Example 2: Factor the Polynomial 6:13
  • Example 3: Solve the Polynomial 8:43
  • Example 4: Solve the Polynomial 13:35