Factoring Polynomials GCF and Quadratic Expressions:
5b^2k^2+25bk^2-250k^2
The answer I figured was GCF for the polynomial is 5 and the GCF for the variable is bk^2. Is this correct.
I see 5k^2 as the GCF, the last term does not contain b
To find the greatest common factor (GCF) of a polynomial, you need to determine the largest term or expression that divides evenly into all the terms.
In your polynomial, 5b^2k^2 + 25bk^2 - 250k^2, the GCF is indeed 5. This is because 5 can be divided evenly into all the coefficients: 5 divides into 5, 25, and 250.
For the variables, you have b^2k^2, bk^2, and k^2. From these, the common variable factors that appear in all the terms are k^2. However, you also have b^2 in one of the terms, so the GCF for the variables should be bk^2, as you correctly mentioned.
Therefore, the GCF for the polynomial is 5bk^2.
If you want to factor out the GCF, you can rewrite the polynomial as follows:
5b^2k^2 + 25bk^2 - 250k^2 = 5bk^2(b + 5) - 250k^2
Now, the polynomial is factored with the GCF factored out. Notice that the remaining terms after factoring out the GCF have a common factor of (b + 5).