Question

2x^4+128 factorise
pls help me with this sum fast ​

Answer 1

Answer:

STEP1:Equation at the end of step 1

2x4 - 128

STEP2:

STEP3:Pulling out like terms

 3.1     Pull out like factors :

   2x4 - 128  =   2 • (x4 - 64) 

Trying to factor as a Difference of Squares:

 3.2      Factoring:  x4 - 64 

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 : 64 is the square of 8

Check :  x4  is the square of  x2 

Factorization is :       (x2 + 8)  •  (x2 - 8) 

Polynomial Roots Calculator :

 3.3    Find roots (zeroes) of :       F(x) = x2+ 8

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

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  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  8. 

 The factor(s) are: 

of the Leading Coefficient :  1

 of the Trailing Constant :  1 ,2 ,4 ,8 

 Let us test ....

  P  Q  P/Q  F(P/Q)   Divisor     -1     1      -1.00      9.00        -2     1      -2.00      12.00        -4     1      -4.00      24.00        -8     1      -8.00      72.00        1     1      1.00      9.00        2     1      2.00      12.00        4     1      4.00      24.00        8     1      8.00      72.00   

Polynomial Roots Calculator found no rational roots

Trying to factor as a Difference of Squares:

 3.4      Factoring:  x2 - 8 

Check : 8 is not a square !! 

Ruling : Binomial can not be factored as the difference of two perfect squares.

Answer 2

1. Common factor

$2 {x}^{4} + 128$

$2{x}^{4} + 64$

2. Find one factor

• Factor by grouping

=

$2 ({x}^{2} - 4x + 8) ({x}^{2} + 4x + 8)$

3. Therefore, your answer is

$2( {x}^{2} - 4x + 8)( {x}^{2} + 4x + 8)$

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