+984 Alright, here we go:
To prove that an expression is never positive, we just need to prove that the maximun value of the expression is smaller than zero.
We can just expand the expression.
\(3(x+1)(x+7)=3x^2+24x+21\)
\((2x+5)^2=4x^2+20x+25\)
\(3x^2+24x+21- (4x^2+20x+25) = -x^2+4x-4\)
Factoring out the negative one, we have:
\( -(x^2-4x+4)\)
Since
\((x^2-4x+4)\)
is a perfect square, we can rewrite the expression like this:
\(-(x-2)^2\)
Since a square is always positive, and a negative of a square is negative, we proved that the original expression is negative, and always will be negative.
I hope this answers your question and you have a wonderful day!
+984 Alright, here we go:
To prove that an expression is never positive, we just need to prove that the maximun value of the expression is smaller than zero.
We can just expand the expression.
\(3(x+1)(x+7)=3x^2+24x+21\)
\((2x+5)^2=4x^2+20x+25\)
\(3x^2+24x+21- (4x^2+20x+25) = -x^2+4x-4\)
Factoring out the negative one, we have:
\( -(x^2-4x+4)\)
Since
\((x^2-4x+4)\)
is a perfect square, we can rewrite the expression like this:
\(-(x-2)^2\)
Since a square is always positive, and a negative of a square is negative, we proved that the original expression is negative, and always will be negative.
I hope this answers your question and you have a wonderful day!
thank you in advance
