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

Question

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

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Eirian 6 months 2021-07-27T11:16:57+00:00 1 Answers 22 views 0

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    2021-07-27T11:18:26+00:00

    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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