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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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Step-by-step explanation:

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3 years ago
Ron wants to buy a video game with a selling price of ?$36?, on sale for? 50% off. The sales tax in his state is 5.5 %. How much
cestrela7 [59]

Answer:

Yes, it costs $18.99.

Step-by-step explanation:

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The sale price is $18.

The state charges 5.5% tax which means you pay 105.5% of the sale price.

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7 0
3 years ago
A savings account earns 7.2 (APR) compounded monthly, so it earns 0.6% each month. Cooper has $1500 in the account now. if he de
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<u>Answer-</u>

<em>Cooper will receive </em><em>$12.00</em><em> at the end of the month.</em>

<u>Solution-</u>

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So the total principal becomes 1500+500 = $2000

Given here,

APR = annual percentage rate = 7.2%

But as we have to calculate the monthly interest, so monthly interest rate would be =\dfrac{7.2}{12}=0.6\%

Time period = 1 month

So, the interest after 1 month will be,

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