1. Factoring Review
Algebra 2

2. Algebra 2 (bell work)
Copy down

3. Tell whether each polynomial is completely factored. If not factor it.
A. 3x2(6x – 4)
B. (x2 + 1)(x – 5)
(x2 + 1)(x – 5)
3x2(6x – 4)
6x2(3x – 2)
6x2(3x – 2) is completely factored.
(x2 + 1)(x – 5) is completely factored.

4. Tell whether the polynomial is completely factored. If not, factor it.
A. 5x2(x – 1)
B. (4x + 4)(x + 1)
5x2(x – 1)
(4x + 4)(x + 1)
5x2(x – 1) is completely factored.
4(x + 1)(x + 1)
4(x + 1)2 is completely factored.

5. Factor 10x2 + 48x + 32 completely. Check your answer.
Check 2(5x + 4)(x + 4) = 2(5x2 + 20x + 4x + 16)
= 10x2 + 40x + 8x + 32
= 10x2 + 48x + 32 

6.  8x6y2 – 18x2y2 Factor 8x6y2 – 18x2y2 completely. Check your answer.
2x2y2(2x2 – 3)(2x2 + 3)
Check 2x2y2(2x2 – 3)(2x2 + 3) = 2x2y2(4x4 – 9)
= 8x6y2 – 18x2y2 

7. 4x3 + 16x2 + 16x Factor each polynomial completely. Check your answer.
Check 4x(x + 2)2 = 4x(x2 + 2x + 2x + 4)
= 4x(x2 + 4x + 4)
= 4x3 + 16x2 + 16x 

8. 8.6
If none of the factoring methods work, the polynomial is said to be unfactorable.
For a polynomial of the form ax2 + bx + c, if there are no numbers whose sum is b and whose product is ac, then the polynomial is unfactorable.
Helpful Hint

9.   9x2 + 3x – 2 Factors of 9 Factors of 2 Outer + Inner 1 and 9
Factor each polynomial completely.
9x2 + 3x – 2
9x2 + 3x – 2
( x )( x ) 
Factors of 9 Factors of Outer + Inner
1 and 9
1 and –2
1(–2) + 1(9) = 7
3 and 3
3(–2) + 1(3) = –3
–1 and 2
3(2) + 3(–1) = 3 
(3x – 1) (3x + 2)

10.   12b3 + 48b2 + 48b Factor each polynomial completely.
Factors of Sum
1 and
2 and  
a = 2 and c = 2
12b(b + 2)(b + 2)
12b(b + 2)2

11.   4y2 + 12y – 72 Factor each polynomial completely. 4(y2 + 3y – 18)
Factors of – Sum
–1 and
–2 and 
–3 and
4(y – 3)(y + 6)

12. (x4 – x2) Factor each polynomial completely. x2(x2 – 1)
x2(x + 1)(x – 1)

14. HW
5.3-
#37-45, 48-54
Solve by factoring