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We appreciate your visit to A greenhouse that specializes in growing geraniums is divided into sections The number of geranium pots in each section depends on the number of sprinklers. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

A greenhouse that specializes in growing geraniums is divided into sections. The number of geranium pots in each section depends on the number of sprinklers in that section.

There are [tex] x(7x − 2) [/tex] pots of red geraniums and [tex] (x + 3)^2 [/tex] pots of pink geraniums in a section with [tex] x [/tex] sprinklers.

Which simplified expression represents the total number of red and pink geranium pots in a section with [tex] x [/tex] sprinklers?

A. [tex] 8x^2 + 4x + 9 [/tex]
B. [tex] 8x^2 + 6x + 9 [/tex]
C. [tex] 8x^2 + 6x + 7 [/tex]
D. [tex] 8x^4 + 4x^2 + 9 [/tex]

Answer :

x(7x-2) = 7x^2-2x
(x+3)^2 = (x+3) (x+3) = x^2 + 6x +9

x^2 - 2x + x^2 + 6x +9 = 8x^2 + 4x + 9

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Rewritten by : Barada

Expression represents the total number of red and pink geranium pots in a section with x sprinklers is equals to 8x² + 4x + 9.

What is quadratic equation?

"Quadratic equation is defined as algebraic expression of single variable with highest degree two."

Formula used

(a + b)² = a² + 2ab + b²

According to the question,

Pots of red geraniums represent by equation x(7x - 2)

Pots of pink geraniums represent by equation (x + 3)²

Total number of red and pink geranium pots in a section with x sprinklers

= x(7x - 2) + (x + 3)²

Open the brackets and apply formula to get quadratic equation we get,

= 7x² - 2x + x² + 6x + 9

= 8x² + 4x + 9

Hence, Option(A) is the correct answer.

Learn more about quadratic equation here

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