Embed Size (px)
Citation preview
Algebra 2: Section 6.4
Factoring and Solving Polynomial Equations
Factoring Quadratics
1. 4x2 24x
4x(x 6)
Common Factor: 4x
Factoring Quadratics
2. 2x2 11x 21
(2x_____)(x_____)
Two factors of -21 that when
FOI LED make the middle
term +11
(2x 3)(x 7)
Factoring Quadratics
23. 4x 36 81x
(2x)2 2 2x 9 (9)2
(2x 9)2
Perfect Square Trinomial
Sum and Difference of Cubes
a3 b3 (a b)(a2 ab b2)
a3 b3 (a b)(a2 ab b2)
x3 64 (x 4)(x2 4x 16)
27x3 8 (3x 2)(9x2 6x 4)
Examples
4. 125 x3
x3 53
(x 5)(x2 5x 52)
(x 5)(x2 5x 25)
Rewrite as sum of cubes
(Changed order, standard)
Factoring by Grouping(used when there are 4 terms)
• Factor common factor out of first two terms
and factor another common factor out of last
two terms
(may need to rearrange)
• Factor common binomial out of each ‘term’
Examples
5. x2y2 3x2 4y2 12
x2(y2 3) 4(y2 3)
(y2 3)(x2 4)
(y2 3)(x 2)(x 2)
Difference of two squares
Examples2 2 3 46. a 8 16b ab b
b2(a2 8ab 16b2)
b2(a 4b)(a 4b)
b2(a 4b)2
Examples47. 25x 36
(5x2)2 (6)2
Difference of two squares
(5x2 6)(5x2 6)
W hich method of factoring?
• 2 terms
• 3 terms
• 4 terms
• Diff. of Squares
• Sum or Diff. of Cubes
• Trial and Error
• Perfect Square Trinomial
• Grouping
Always look for common
factor!!
Solving Polynomial Equations by
Factoring
(Examples)58. 2 18 0y y
42 ( 9) 0y y2 22 ( 3)( 3) 0y y y
Difference of two squares
2 22 0 3 0 3 0y or y or y
0 3 3y or y or y i
0 3y or yFor this assignment,
only concerned with
real solut ions
More Examples5 29. 4 108 0x x
2 34 ( 27) 0x x2 24 ( 3)( 3 9) 0x x x x
Difference of two cubes
2 24 0 3 0 3 9 0x or x or x x
3 9 4(1)(9)0 3
2x or x or x
0 3x or xThis is going to be
imaginary.
The discriminant is
negative!
Assignment
• p.349
# 33-85 all, 87, 88
(55 problems)
• Due W ednesday!
