Factor Completely: I am really confused on how to start it.
12q^5w^2-36q^4w^3-120q^3w^4
Help please. :)
Factor out 12q^3w^2:
12q^3w^2(q^2 - 3qw - 10w^2)
Can we factor further? Yes.
q^2 - 3qw - 10w^2 factors are (q - 5w)(q + 2w).
We end up with this:
12q^3w^2(q - 5w)(q + 2w)
And that's as far as we can factor on this one!
I hope this will help.
fudge
To factor the expression 12q^5w^2 - 36q^4w^3 - 120q^3w^4 completely, you can follow these steps:
Step 1: Look for the greatest common factor (GCF) among the terms. In this case, the GCF is 12q^3w^2.
Step 2: Factor out the GCF from each term:
12q^5w^2 / (12q^3w^2) = q^2
-36q^4w^3 / (12q^3w^2) = -3qw
-120q^3w^4 / (12q^3w^2) = -10w^2
Step 3: Rewrite the expression using the factored GCF and the remaining terms:
12q^5w^2 - 36q^4w^3 - 120q^3w^4 = 12q^3w^2(q^2 - 3qw - 10w^2)
Step 4: Determine if the remaining factor is further factorable. In this case, we can factor the quadratic expression q^2 - 3qw - 10w^2.
Step 5: Find two numbers that multiply to -10 and add up to -3. These numbers are -5 and 2.
Thus, q^2 - 3qw - 10w^2 = (q - 5w)(q + 2w).
Finally, combining all the factors, we get the completely factored expression:
12q^5w^2 - 36q^4w^3 - 120q^3w^4 = 12q^3w^2(q - 5w)(q + 2w)
And that's how you factor the given expression completely.