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 x(7x − 2) pots of red geraniums and (x + 3)^2 pots of pink geraniums in a section with x sprinklers.

Which simplified expression represents the total number of red and pink geranium pots in a section with x sprinklers?
A. 8x^2 + 4x + 9
B. 8x^2 + 6x + 9
C. 8x^2 + 6x + 7
D. 8x^4 + 4x^2 + 9

Question

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Respuesta :

indirasingh03 indirasingh03 · Answer 1 · 2017-07-07T19:37:57+02:00

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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Yogeshkumari Yogeshkumari · Answer 2 · 2022-06-09T20:20:33+02:00

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

"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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