Question
Factor out the GCF from the following polynomial. \( 32 m^{7}-96 m^{6}+144 m^{5}-104 m^{3} \) \( 32 m^{7}-96 m^{6}+144 m^{5}-104 m^{3}=\square \)
Ask by Newton Bates.
Feb 16,2025 13:01
UpStudy AI Solution
Tutor-Verified Answer
Answer
The factored form is \(8m^{3}(4m^{4}-12m^{3}+18m^{2}-13)\).
Solution
Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.
Unlock Answered by UpStudy AI and reviewed by a Professional Tutor
Like
Beyond the Answer
To factor out the greatest common factor (GCF) from the polynomial \( 32 m^{7}-96 m^{6}+144 m^{5}-104 m^{3} \), we first identify the GCF of the coefficients (32, -96, 144, -104), which is 16. The lowest power of \( m \) present in all terms is \( m^{3} \). Thus, the GCF is \( 16m^{3} \).
Now, we can factor it out:
\[
32 m^{7}-96 m^{6}+144 m^{5}-104 m^{3} = 16m^{3}(2m^{4}-6m^{3}+9m^{2}-6)
\]
This gives us the factored form of the polynomial.
So, the equation can be completed as follows:
\( 32 m^{7}-96 m^{6}+144 m^{5}-104 m^{3}= 16m^{3}(2m^{4}-6m^{3}+9m^{2}-6) \)
Related Questions
Find the equation (in terms of x) of the line through the points (-2,4) and (4,-14). y=
Algebra
Mar 24, 2025
Identifica cuáles de los siguientes polinomios están bien definidos: a. P(x)=5 x^3+1 / 2 x^2-x, b. Q(x)=x+1, c. R(x)=3 x^(-2)-5 x+6, d. M(x)=7x, e. A(x)=2 x^3+x^(1 / 2)-3, f. I(x)=3 x^2-5 x+6, g. C(x)=-3mnx-6nm x^2, h. D(x)=x^5-1/4 x-1, i. G(x)=-3 x^(-2)+8 x^(-5)-4, j. F(x)=-6
Algebra
Mar 30, 2025
7. Resuelvo las siguientes ecuaciones de segundo grado, factorizadas y fracciones algobraicas. a) x^{2} - x/2 = 1/3 - 2x/3 b) x^{2}/2-3x/5 = 1/5-x/6 c) 6(x+2)^{2} = 13(x+1)(x+2) d) (2x+1)(x+1) = 5(x+1) e)(4x^{2}-1)(x-5) = 0 f) x/(x+2) = 1/2(x-1)
Algebra
Mar 25, 2025
Write (9m)^4 without exponents.
Algebra
Mar 28, 2025
