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olya-2409 [2.1K]
3 years ago
11

Factor 3a^3 + 18a² + 8a + 48 completely.

Mathematics
1 answer:
fomenos3 years ago
3 0

Answer:

(3a2 + 8) • (a - 6)

Step-by-step explanation:

STEP 1:

Equation at the end of step 1

 (((3 • (a3)) -  (2•32a2)) +  8a) -  48

STEP  2:

Equation at the end of step 2:

 ((3a3 -  (2•32a2)) +  8a) -  48

STEP 3:

Checking for a perfect cube

3.1    3a3-18a2+8a-48  is not a perfect cube

Trying to factor by pulling out :

3.2      Factoring:  3a3-18a2+8a-48

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

Group 1:  8a-48

Group 2:  -18a2+3a3

Pull out from each group separately :

Group 1:   (a-6) • (8)

Group 2:   (a-6) • (3a2)

              -------------------

Add up the two groups :

              (a-6)  •  (3a2+8)

Which is the desired factorization

Polynomial Roots Calculator :

3.3    Find roots (zeroes) of :       F(a) = 3a2+8

Polynomial Roots Calculator is a set of methods aimed at finding values of  a  for which   F(a)=0  

It would only find Rational Roots that is numbers  a  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  3  and the Trailing Constant is  8.

The factor(s) are:

of the Leading Coefficient :  1,3

of the Trailing Constant :  1 ,2 ,4 ,8

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If the ratio of the sides of two squares is 3:1, what is the ratio of their perimeters?
Anvisha [2.4K]

Answer:

Ratio of the perimeters =3:1

Step-by-step explanation:

We have given that : Ratio of the sides of two squares is 3:1

To find : Ratio of their perimeters

Solution : Let the length of the sides are 3:1 = 3x : x

                  Formula of perimeter of square = 4(side)

Using the formula ,

Perimeter of 1 square = 4×3x= 12x

Perimeter of 2 square = 4×x= 4x

Ratio of the perimeter of 1 square and 2 square = 12x : 4x

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8 0
3 years ago
A seagull was flying about sea level looking to catch a fish below sea level. The elevation above sea level was 125 1/2 feet. He
frez [133]

Answer:

The seagull's position halfway is 85.5 feet.

Step-by-step explanation:

The seagull is at 125 1/2 feet above the sea level.

The fish is at 45 1/2 feet below the sea level.

The distance between the seagull and fish = seagull's distance above the sea level + fish's distance below the sea level

                                                  = 125 1/2 + 45 1/2

                                                  = \frac{251}{2} + \frac{91}{2}

                                                  = \frac{342}{2}

                                                  = 171

The distance between the seagull and fish is 171 feet.

Since the seagull stops halfway, then;

seagull's position = \frac{171}{2}

                             = 85.5

The seagull's position halfway is 85.5 feet.

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