Factor f(x)= x^4 - 24x^2 -25 (show full steps)

Find real and non-real solutions

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

 (22x2 -  24x) +  37  = 0  

STEP

2

:

Trying to factor by splitting the middle term

2.1     Factoring  4x2-24x+37  

The first term is,  4x2  its coefficient is  4 .

The middle term is,  -24x  its coefficient is  -24 .

The last term, "the constant", is  +37  

Step-1 : Multiply the coefficient of the first term by the constant   4 • 37 = 148  

Step-2 : Find two factors of  148  whose sum equals the coefficient of the middle term, which is   -24 .

     -148    +    -1    =    -149  

     -74    +    -2    =    -76  

     -37    +    -4    =    -41  

     -4    +    -37    =    -41  

     -2    +    -74    =    -76  

     -1    +    -148    =    -149  

     1    +    148    =    149  

     2    +    74    =    76  

     4    +    37    =    41  

     37    +    4    =    41  

     74    +    2    =    76  

     148    +    1    =    149  

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

2

:

 4x2 - 24x + 37  = 0

it has the same slope and a different y-intercept

hope this : )