1. Bell Ringer
Factor the following:
81x3
– 192
a) 3(3x - 4)(9x2
+ 4x + 16)
b) (3x- 4)(9x2
+ 4x + 16)
c) 3(3x - 4)(9x2
+ 12x + 16)
d) (9x - 4)(9x2
+ 4x + 16)
Students will be able
to factor polynomial
equations.
Page 356
#18-29,
32-40 (even)

2. Today’s Lesson
Goal: Factor by Grouping & Factor
Polynomials into Quadratic Form
• Factor by Grouping - factors out common
terms, and then groups them.
• For polynomials raised to higher powers,
such as to the fourth power, we can factor
into two quadratics.

3. Factor by Grouping
Pattern:
ra + rb +sa +sb = r(a + b) + s(a + b)
=(r + s)(a + b)

4. Factor by Grouping
• Example 1:
x3
– 3x2
–16x + 48
x2
(x-3) – 16(x – 3)
(x2
– 16)(x-3)

5. Factor by Grouping Exercises
x3
+ 2x2
+ 3x + 6 m3
– 2m2
+ 4m – 8

6. Factor into Quadratic Form
• Recall a quadratic is of the form:
ax2
+ bx2
+ c
• Sometimes with higher powers, we
factor our polynomial into quadratic form.
• Example: x4
– 81
Think of rewriting x4
as (x2
)2
= (x2
+ 9)(x2
– 9)
= (x2
+ 9)(x + 3)(x – 3)

7. Factor into Quadratic Form
16x4
– 81 6y6
– 5y3
– 4

8. Factor into Quadratic Form
• Example 2:
2x8
+ 10x5
+ 12x2
Factor common monomial
= 2x2
(x6
+ 5x3
+ 6)
Factor our trinomial
= 2x2
(x3
+ 3)(x3
+ 2)

9. Challenge Problem
• The dimensions of a jewelry box are:
length 4x, width (x-1), and height (x-2).
If the volume of the box is 24 cubic
inches, find the dimensions of the box.
• Hint: Remember V=lwh. Multiply this
out, and then try factoring by grouping
to solve.
• State the new dimensions,
and show all of your work.

10. Challenge Problem
volume 24 in3
, length 4x, width (x-1), height (x-2)

11. Minute Paper
1) What was the most important topic
you learned today?
2) What did you like/dislike about the
lesson?
3) How could I improve it?

12. Homework
Page 356
#18-29; 32-40 (even)
Factor by Grouping
Factoring into Quadratics
Solve by Factoring