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3 years ago

Factor x3 + x2 + x + 1 by grouping.

Mathematics

2 answers:

Keith_Richards [23]3 years ago

7 0

Should be the answer
l
l
v
(x+1)(x2+2)

kykrilka [37]3 years ago

4 0

To factor by grouping, you have to divide the problem into two groups:
x^3+x^2+x+1
(x^3+x^2)+(x+1)
Factor each group individually
(x^3+x^2)+(x+1)
x^2(x+1)+(x+1)
(x^2+1)(x+1)

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Answer:

$\sf \dfrac{1}{4} \pi \quad or \quad \dfrac{7}{9}$

Step-by-step explanation:

The width of a square is its side length.

The width of a circle is its diameter.

Therefore, the largest possible circle that can be cut out from a square is a circle whose diameter is equal in length to the side length of the square.

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$\sf \textsf{Area of a square}=s^2 \quad \textsf{(where s is the side length)}$

$\sf \textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}$

$\sf \textsf{Radius of a circle}=\dfrac{1}{2}d \quad \textsf{(where d is the diameter)}$

If the diameter is equal to the side length of the square, then:
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Therefore:

$\begin{aligned}\implies \sf Area\:of\:circle & = \sf \pi \left(\dfrac{s}{2}\right)^2\\& = \sf \pi \left(\dfrac{s^2}{4}\right)\\& = \sf \dfrac{1}{4}\pi s^2 \end{aligned}$