Which of the following expressions equals the sum of the binomial factors of 6q^3-5q^2+24q-20?
A. 7q^3-1
B. 6q^3-1
c. q^2+6q-1
D. q^2+6q+1
To find the sum of the binomial factors of the given expression, we need to factorize it first. Let's factorize the expression 6q^3 - 5q^2 + 24q - 20.
First, we can look for a common factor among all the terms. The greatest common factor (GCF) of the expression is 1, so there is no common factor to factor out.
Next, we can try to factor by grouping. Group the terms in pairs:
(6q^3 - 5q^2) + (24q - 20)
Notice that we can factor out a common term from the first pair:
q^2(6q - 5) + (24q - 20)
Now, let's try to look for another common factor between the two terms. In this case, we can factor out 4:
q^2(6q - 5) + 4(6q - 5)
Now we can see that there is a common binomial factor, (6q - 5), in both terms. Let's factor it out:
(6q - 5)(q^2 + 4)
Therefore, the sum of the binomial factors of 6q^3 - 5q^2 + 24q - 20 is (6q - 5) + (q^2 + 4) = 6q - 5 + q^2 + 4.
Now, let's compare the given answer choices:
A. 7q^3 - 1
B. 6q^3 - 1
C. q^2 + 6q - 1
D. q^2 + 6q + 1
Out of these options, option C, q^2 + 6q - 1, matches the sum of the binomial factors we found earlier, which is 6q - 5 + q^2 + 4.
Therefore, the answer is C. q^2 + 6q - 1.