jjrocks170 said:
We have a test tomorrow, and this is about how far I got in this expression:
(g^2+10g+25)
Can anyone help me with this expression? :?
Thanks! :mrgreen:
A quadratic function
\(\displaystyle f(x) = a \cdot x^2 + b \cdot x + c\)
can be factored as:
\(\displaystyle f(x) \, = \, a \cdot x^2 + b \cdot x + c\, = a\cdot (x - x_1)\cdot (x - x_2)\)
where
\(\displaystyle x_{1} = \frac{-b \, + \, \sqrt{b^2 - 4\cdot a \cdot c}}{2\cdot a}\)
and
\(\displaystyle x_{2} = \frac{-b \, - \, \sqrt{b^2 - 4\cdot a \cdot c}}{2\cdot a}\)
However, your problem has a
special form - you
need not calculate this way.
recall
\(\displaystyle (a\, +\, b)^2\, = \, a^2\, +\, 2\cdot a\cdot b \, +\, b^2\)
so
\(\displaystyle g^2 \, +\, 10\cdot g \,+\, 25\, =\,g^2 \, +\, 2\cdot\,5\,\cdot g \,+\, 5^2\, =\,(g\, + \, 5)^2\, =\, (g\, + \,5)\cdot (g\, + \,5)\)