Asked by Victoria Grose on May 15, 2024
Verified
Solve the equation below by factoring. c3+2c2−4c−8=0c ^ { 3 } + 2 c ^ { 2 } - 4 c - 8 = 0c3+2c2−4c−8=0
A) c=0c = 0c=0 and c=2c = 2c=2
B) c=−2c = - 2c=−2 , c=0c = 0c=0 , and c=2c = 2c=2
C) c=−2c = - 2c=−2
D) c=−2c = - 2c=−2 and c=2c = 2c=2
E) c=−2c = - 2c=−2 and c=0c = 0c=0
Factoring
The process of breaking down an expression into a product of simpler elements or factors.
- Comprehend and utilize the concepts of polynomial factoring to resolve equations.
- Examine and decompose polynomials of higher degrees to identify their zeros.
- Understand the relationship between the zeros of polynomial functions and their factored forms.
Verified Answer
MD
Michael DeboodtMay 19, 2024
Final Answer :
D
Explanation :
We can factor the equation as follows: c3+2c2−4c−8=(c3−2c)+(2c2−4)=c(c2−2)+2(c2−2)=(c+2)(c−2)(c2+2c+4)=0.c^3 + 2c^2 - 4c - 8 = (c^3 - 2c) + (2c^2 - 4) = c(c^2 - 2) + 2(c^2 - 2) = (c+2)(c-2)(c^2+2c+4) = 0.c3+2c2−4c−8=(c3−2c)+(2c2−4)=c(c2−2)+2(c2−2)=(c+2)(c−2)(c2+2c+4)=0. Therefore, the solutions are $c=-2$ and $c=2.$
Learning Objectives
- Comprehend and utilize the concepts of polynomial factoring to resolve equations.
- Examine and decompose polynomials of higher degrees to identify their zeros.
- Understand the relationship between the zeros of polynomial functions and their factored forms.