Factor the polynomial completely using any method

Question

2. 2a^3 + 432

4. -3c^3 + 24

16. 2ac^2 - 5bc^2 - 2ad^2 + 5bd^2

12. 6b^4 - 17b^2 - 28

 

 

 

Answer 1

2)

 

2a³ + 432 =

 

2(a³ + 216)

 

We know that the cube-root of 216 is 6.  So a factor of (a³ + 216) must be either (a - 6) or (a + 6).  If we use division, the factor that gives us a remainder of zero is (a + 6).

 

2(a + 6)(a² - 6a + 36)

 

 

4)

 

-3c³ + 24 =

 

-3(c³ - 8)

 

The cube-root of 8 is 2.  So a factor of (c³ - 8) must be either (c + 2) or (c - 2).  We pick the factor that gives us a remainder of zero when division is used here.

 

 

-3(c - 2)(c² + 2c + 4)

 

 

 

16)

 

Factor by grouping.

 

c²(2a - 5b) - d²(2a - 5b) =

 

(2a - 5b)(c² - d²) =

 

(2a - 5b)(c - d)(c + d)

 

 

12)

 

Factor using FOIL method.

 

6b⁴ - 17b² - 28

 

(6b² + 7)(b² - 4)