Question

factorise the following expression using the method of grouping term. (a) a³–4a²+3a–12​

Answer 1

Answer:(a2 + 3) * (a - 4)

Step-by-step explanation:

Changes made to your input should not affect the solution:

(1): "a2"   was replaced by   "a^2".  1 more similar replacement(s).

STEP

1

:

Equation at the end of step 1

 (((a3) -  22a2) +  3a) -  12

STEP

2

:

Checking for a perfect cube

2.1    a3-4a2+3a-12  is not a perfect cube

Trying to factor by pulling out :

2.2      Factoring:  a3-4a2+3a-12  

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

Group 1:  3a-12  

Group 2:  -4a2+a3  

Pull out from each group separately :

Group 1:   (a-4) • (3)

Group 2:   (a-4) • (a2)

              -------------------

Add up the two groups :

              (a-4)  •  (a2+3)  

Which is the desired factorization

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

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

Rational Roots Test is one of the above mentioned tools. 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  1  and the Trailing Constant is  3.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,3

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        4.00      

     -3       1        -3.00        12.00      

     1       1        1.00        4.00      

     3       1        3.00        12.00

Answer 2

Answer:

$\\ {a}^{2}(a - 4) + 3(a - 4) \\ = ( {a }^{2} + 3)(a - 4)$