Which terms and 45p4q have a GCF of 9p3? Check all that apply.
*18p3r
x27p4q
x36p3q6
*63p3
x72p3q6
The ones with the stars next to them are the correct ones and the ones with the x next to them are the wrong ones.
Does answer choice A make any sense to any of you people out there. In case you can't see it answer choice A has an r in it but the original equations doesn't. Please explain how this makes sense.
i didnt die for this
The first step to determining which terms have a Greatest Common Factor (GCF) of 9p^3 with 45p^4q is to factor both numbers.
Factorizing 45p^4q:
45p^4q can be broken down into 9 * 5 * p^4 * q.
Now we can compare the factors with the GCF 9p^3.
For a term to have a GCF of 9p^3 with 45p^4q, it must include:
- A factor of 9 (because 9 is part of the GCF)
- A factor of p^3 (because p^3 is part of the GCF)
- And any other factors present in 45p^4q.
Let's analyze each answer choice:
A) 18p^3r: This term includes a factor of 18 (which is 2 * 9), p^3, and 'r.' However, the original expression does not have an 'r', so A is not a correct answer.
B) 27p^4q: This term includes a factor of 27 (which is 3 * 9), p^4, and q. All the factors from 45p^4q are present here, so B is a correct answer.
C) 36p^3q^6: This term includes a factor of 36 (which is 4 * 9), p^3, q^6, and additional factors not present in 45p^4q. Therefore, C is not a correct answer.
D) 63p^3: This term includes a factor of 63 (which is 7 * 9), p^3, and no additional factors. All the factors from 45p^4q are present here, so D is a correct answer.
E) 72p^3q^6: This term includes a factor of 72 (which is 8 * 9), p^3, q^6, and additional factors not present in 45p^4q. Therefore, E is not a correct answer.
So, the correct answer choices are B) 27p^4q and D) 63p^3.