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notsponge [240]
3 years ago
10

Find the sum. Write your answer in standard form.

Mathematics
1 answer:
jeyben [28]3 years ago
5 0
(4x3+2x+6)+(2x3-x2+2)

Final result :

6x3 - x2 + 2x + 8
Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2". 2 more similar replacement(s).

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(((4•(x3))+2x)+6)+((2x3-x2)+2)
Step 2 :

Equation at the end of step 2 :

((22x3 + 2x) + 6) + (2x3 - x2 + 2)
Step 3 :

Checking for a perfect cube :

3.1 6x3-x2+2x+8 is not a perfect cube

Trying to factor by pulling out :

3.2 Factoring: 6x3-x2+2x+8

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: 2x+8
Group 2: 6x3-x2

Pull out from each group separately :

Group 1: (x+4) • (2)
Group 2: (6x-1) • (x2)
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Note that while the figure is made up of rectangle and parallelogram, then the area of this figure

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1. The area of rectangle is

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The vertices of rectangle are points A(-2,-2), B(0,-6), C(8,-2) and F(6,2). Then

AB=\sqrt{(-2-0)^2+(-2+6)^2}=\sqrt{4+16}=\sqrt{20}=2\sqrt{5},\\ \\BC=\sqrt{(8-0)^2+(-2+6)^2}=\sqrt{64+16}=\sqrt{80}=4\sqrt{5}.

Therefore,

A_{rectangle\ ABCF}=2\sqrt{5}\cdot 4\sqrt{5}=8\cdot 5=40\ un.^2

2. The area of parallelogram can be calculated using formula

A_{parallelogram\ FCDE}=\text{base}\cdot \text{height}.

The base of parallelogram is segment CD with length

CD=\sqrt{(8-8)^2+(3+2)^2}=\sqrt{25}=5

and the height has length 2 un. Then

A_{parallelogram\ FCDE}=5\cdot 2=10\ un^2.

3. Now

A_{figure}=40+10=50\ un.^2

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