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raketka [301]
3 years ago
12

How do you factor this expression: x^3 + 9x^2 + 27x + 27. Thanks! :)

Mathematics
1 answer:
soldier1979 [14.2K]3 years ago
5 0

Answer:

(x + 3)³

Step-by-step explanation:

Use rational root test to check for possible rational roots.

Factors of 27 are 1, 3, 9, and 27.

Factors of 1 are 1.

Possible rational roots are:

±1/1, ±3/1, ±9/1, ±27/1

Checking each one, we find that -3 is a root.  So x + 3 is a factor.

Knowing that, we can use grouping to factor.

x³ + 9x² + 27x + 27

x³ + 9x² + 18x + 9x + 27

x (x² + 9x + 18) + 9 (x + 3)

x (x + 6) (x + 3) + 9 (x + 3)

(x + 3) (x (x + 6) + 9)

(x + 3) (x² + 6x + 9)

(x + 3) (x + 3)²

(x + 3)³

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A company pays its employees a fixed base salary and a commission based on sales. The scatter plot below shows the total earning
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I'm assuming the question is

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How many 2-digit numbers are multiples of 7 or 5
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2 years ago
Given: <br> PQ<br> ⊥<br> QR<br> , PR=20,<br> SR=11, QS=5<br> Find: The value of PS.
dlinn [17]

Answer:

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Step-by-step explanation:

In this question we have two right triangles. Triangle PQR and Triangle PQS.

Where S is some point on the line segment QR.

Given:

PR = 20

SR = 11

QS = 5

We know that QR = QS + SR

QR = 11 + 5

QR = 16

Now triangle PQR has one unknown side PQ which in its base.

Finding PQ:

Using Pythagoras theorem for the right angled triangle PQR.

PR² = PQ² + QR²

PQ = √(PR² - QR²)

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Now for right angled triangle PQS, PS is unknown which is actually the hypotenuse of the right angled triangle.

Finding PS:

Using Pythagoras theorem, we have:

PS² = PQ² + QS²

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Answer:

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In this case since the base of the exponent equals 2, that means r=1, since 1+1=2. This means it has a growth rate of 100%, which makes sense, since the base is 2, meaning it doubles or increases by 100% every time x increases by 1.

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2 years ago
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