Question

a4 - 5a2 - 36 factorise​

Answer 1

Answer:

4-5-38.......:.....:

Answer 2

Answer:

Step-by-step explanation:

a4-5a2-36  

Final result :

 (a2 + 4) • (a + 3) • (a - 3)

Reformatting the input :

Changes made to your input should not affect the solution:

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

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 ((a4) -  5a2) -  36

Step  2  :

Trying to factor by splitting the middle term

2.1     Factoring  a4-5a2-36  

The first term is,  a4  its coefficient is  1 .

The middle term is,  -5a2  its coefficient is  -5 .

The last term, "the constant", is  -36  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -36 = -36  

Step-2 : Find two factors of  -36  whose sum equals the coefficient of the middle term, which is   -5 .

     -36    +    1    =    -35  

     -18    +    2    =    -16  

     -12    +    3    =    -9  

     -9    +    4    =    -5    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  4  

                    a4 - 9a2 + 4a2 - 36

Step-4 : Add up the first 2 terms, pulling out like factors :

             a2 • (a2-9)

             Add up the last 2 terms, pulling out common factors :

                   4 • (a2-9)

Step-5 : Add up the four terms of step 4 :

                   (a2+4)  •  (a2-9)

            Which is the desired factorization

Polynomial Roots Calculator :

2.2    Find roots (zeroes) of :       F(a) = a2+4

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  4.  

The factor(s) are:  

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,4  

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        5.00      

     -2       1        -2.00        8.00      

     -4       1        -4.00        20.00      

     1       1        1.00        5.00      

     2       1        2.00        8.00      

     4       1        4.00        20.00      

Polynomial Roots Calculator found no rational roots

Trying to factor as a Difference of Squares :

2.3     Factoring:  a2-9  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =  

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.  

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 9 is the square of 3

Check :  a2  is the square of  a1  

Factorization is :       (a + 3)  •  (a - 3)  

Final result :

 (a2 + 4) • (a + 3) • (a - 3)

Processing ends successfully.

hope it's helpful

aaliyafridi