A school is installing a flagpole in the central plaza. The plaza is a square with side length 100 yards as shown in the figure below. The flagpole will take up a square plot in the middle of the plaza and its base will have an area of x^2−6x+9 yd^2.

Area of the flagpole plot: x^2−6x+9

Find the length of the base of the flagpole by factoring. (Hint: Because the area of the flagpole is an expression that involves the variable x, the length of the base will also involve the variable x.)

The length of the base of the flagpole is

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boffeemadrid boffeemadrid · Answer 1 · 2020-11-13T15:13:33+01:00

Answer:

[tex]x-3[/tex]

Step-by-step explanation:

The area of the flagpole base is [tex]x^2-6x+9\ \text{yd}[/tex]

where the factor of the equation is the length of the base.

In order to find the length we need to factorize the equation

[tex]x^2-6x+9[/tex]

[tex]=x^2-3x-3x+9[/tex]

[tex]=x(x-3)-3(x-3)[/tex]

[tex]=(x-3)(x-3)[/tex]

The length of the base of the flagpole is [tex](x-3)\ \text{yd}[/tex].

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MrRoyal MrRoyal · Answer 2 · 2021-11-09T21:39:15+01:00

The area of a square base is the product of the side lengths.

The length of the base is x - 3

The area is given as:

[tex]\mathbf{Area =x^2 - 6x + 9}[/tex]

Expand

[tex]\mathbf{Area =x^2 - 3x - 3x + 9}[/tex]

Factorize

[tex]\mathbf{Area =x( x- 3) - 3(x - 3)}[/tex]

Factor out x - 3

[tex]\mathbf{Area =( x- 3) (x - 3)}[/tex]

Express as squares

[tex]\mathbf{Area =( x- 3)^2}[/tex]

Rewrite the area as:

[tex]\mathbf{Length^2 =( x- 3)^2}[/tex]

Take square roots of both sides

[tex]\mathbf{Length =x- 3}[/tex]

Hence, the length of the base is x - 3