#### jjrocks170

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(g^2+10g+25)

Can anyone help me with this expression? :?

Thanks! :mrgreen:

- Thread starter jjrocks170
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(g^2+10g+25)

Can anyone help me with this expression? :?

Thanks! :mrgreen:

- Joined
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To learn how to factor quadratics (sometimes also called trinomials), please consider studying some of the many great lessons available online. :idea:jjrocks170 said:(g^2+10g+25)

Can anyone help me with this expression?

. . . . .

. . . . .

Once you have studied some lessons and have learned the basic terms and techniques, please attempt the exercise. If you get stuck, or if you are unsure of your steps or solution, kindly reply showing all of your work and reasoning. Thank you!

Eliz.

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A quadratic functionjjrocks170 said:

(g^2+10g+25)

Can anyone help me with this expression? :?

Thanks! :mrgreen:

\(\displaystyle f(x) = a \cdot x^2 + b \cdot x + c\)

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

recall

\(\displaystyle (a\, +\, b)^2\, = \, a^2\, +\, 2\cdot a\cdot b \, +\, b^2\)

so

\(\displaystyle g^2 \, +\, 10\cdot g \,+\, 25\, =\,g^2 \, +\, 2\cdot\,5\,\cdot g \,+\, 5^2\, =\,(g\, + \, 5)^2\, =\, (g\, + \,5)\cdot (g\, + \,5)\)