What is the complete factored form of the following polynomial?
40u^2v + 50uv^2
a) 10u(4uv + 10v^2)
b) 5u(8uv + 10v^2)
c) 10uv(4u + 5v)
d) 5v(8u^2 +10uv)
Thanks!!!!!!!!!!!!!!!
C. What both of those have in common is a 10uv, which can be taken out and what's left is the 4u+5v.
Thank you Jen :)
To find the complete factored form of the polynomial 40u^2v + 50uv^2, we need to look for the greatest common factor (GCF) of the terms and factor it out.
Step 1: Find the GCF of the terms
The GCF of 40u^2v and 50uv^2 is 10uv. To find the GCF, we find the highest power of each variable that appears in both terms, and take the product of those powers.
Step 2: Divide each term by the GCF
Dividing 40u^2v by 10uv gives us 4u, and dividing 50uv^2 by 10uv gives us 5v.
Step 3: Write the factored form
The factored form of the polynomial is the GCF multiplied by the quotient from step 2. In this case, the GCF is 10uv, and the quotient is 4u + 5v.
Therefore, the complete factored form of 40u^2v + 50uv^2 is 10uv(4u + 5v), which corresponds to option c).