Asked by Jenna Montgomery on Mar 10, 2024
Verified
Factor the perfect square trinomial 4m3−72m2+324m4 m ^ { 3 } - 72 m ^ { 2 } + 324 m4m3−72m2+324m .
A) 4m(m+9) 24 m ( m + 9 ) ^ { 2 }4m(m+9) 2
B) 4(m+9) 34 ( m + 9 ) ^ { 3 }4(m+9) 3
C) 4m(m−9) 24 m ( m - 9 ) ^ { 2 }4m(m−9) 2
D) 4(m−9) 34 ( m - 9 ) ^ { 3 }4(m−9) 3
E) 4m(m2−9) 4 m \left( m ^ { 2 } - 9 \right) 4m(m2−9)
A) 4m(m+9) 24 m ( m + 9 ) ^ { 2 }4m(m+9) 2
B) 4(m+9) 34 ( m + 9 ) ^ { 3 }4(m+9) 3
C) 4m(m−9) 24 m ( m - 9 ) ^ { 2 }4m(m−9) 2
D) 4(m−9) 34 ( m - 9 ) ^ { 3 }4(m−9) 3
E) 4m(m2−9) 4 m \left( m ^ { 2 } - 9 \right) 4m(m2−9)
Perfect Square Trinomial
A trinomial that can be factored into a binomial squared, typically in the form \(a^2 + 2ab + b^2\) or \(a^2 - 2ab + b^2\).
- Apply techniques to factor perfect square trinomials.
Verified Answer
KN
Kelly Nicole
Mar 10, 2024
Final Answer :
C
Explanation :
The trinomial can be factored by first factoring out the greatest common factor, which is 4m4m4m , resulting in 4m(m2−18m+81)4m(m^2 - 18m + 81)4m(m2−18m+81) . The expression inside the parentheses is a perfect square trinomial, factoring to (m−9)2(m - 9)^2(m−9)2 . Thus, the complete factorization is 4m(m−9)24m(m - 9)^24m(m−9)2 .
Learning Objectives
- Apply techniques to factor perfect square trinomials.