Carcass wrote:
\(y>9\)
\(z>2\)
Quantity A |
Quantity B |
\(x^2yz-8x^2z+3yz-24z\) |
\(0\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
This is a tricky question, but with some factoring we can make sense of it.
\(x^2yz-8x^2z+3yz-24z\)
First, notice that \(x^2yz-8x^2z\) has common factors of \(x^2\) and \(z\), so lets factor those out.
\(x^2z(y-8)+3yz-24z\)
Now notice that \(3yz-24z\) has common factors of \(3\) and \(z\), so let's factor those out:
\(x^2z(y-8)+3z(y-8)\)
From here, we can factor out a factor \((y-8)\):
\((y-8)(x^2z+3z)\)
Then from here we can factor out a factor of \(z\) from \((x^2z+3z)\):
\((y-8)(z)(x^2+3)\)
Since \(y > 9\), \(y - 8 > 0\), so the \((y-8)\) portion of that equation is positive.
Since \(z > 2\), we know that the \((z)\) portion of that equation is positive.
Finally, since \(x^2\) is always positive or 0, and \(3\) is positive, \((x^2+3)\) is positive.
So we have a
positive*positive*positive in Quantity A, and 0 in Quantity B.
Therefore, Quantity A is greater.