Q:

factor by grouping 2m^3+6m^2+3m+9​

Accepted Solution

A:
Answer:Step-by-step explanation:Final result :  (2m2 + 3) • (m + 3) Reformatting the input : Changes made to your input should not affect the solution: (1): "m2"   was replaced by   "m^2".  1 more similar replacement(s). Step by step solution : Step  1  : Equation at the end of step  1  :  (((2 • (m3)) +  (2•3m2)) +  3m) +  9 Step  2  : Equation at the end of step  2  :  ((2m3 +  (2•3m2)) +  3m) +  9 Step  3  : Checking for a perfect cube : 3.1    2m3+6m2+3m+9  is not a perfect cube   Trying to factor by pulling out : 3.2      Factoring:  2m3+6m2+3m+9   Thoughtfully split the expression at hand into groups, each group having two terms : Group 1:  3m+9  Group 2:  6m2+2m3   Pull out from each group separately : Group 1:   (m+3) • (3) Group 2:   (m+3) • (2m2)               ------------------- Add up the two groups :               (m+3)  •  (2m2+3)  Which is the desired factorization Polynomial Roots Calculator : 3.3    Find roots (zeroes) of :       F(m) = 2m2+3 Polynomial Roots Calculator is a set of methods aimed at finding values of  m  for which   F(m)=0   Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  m  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  2  and the Trailing Constant is  3.   The factor(s) are:   of the Leading Coefficient :  1,2   of the Trailing Constant :  1 ,3   Let us test ....   P    Q    P/Q    F(P/Q)     Divisor      -1       1        -1.00        5.00            -1       2        -0.50        3.50            -3       1        -3.00        21.00            -3       2        -1.50        7.50            1       1        1.00        5.00            1       2        0.50        3.50            3       1        3.00        21.00            3       2        1.50        7.50       Polynomial Roots Calculator found no rational roots Final result :  (2m2 + 3) • (m + 3) Processing ends successfully Subscribe to our mailing list