10x^5+5x^3-14x^2-7
factor expression

Step-by-step explanation:

10x5+5x3-14x2-7  

 (5x3 - 7) • (2x2 + 1)

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (((10•(x5))+(5•(x3)))-(2•7x2))-7

Step  2  :

Equation at the end of step  2  :

 (((10 • (x5)) +  5x3) -  (2•7x2)) -  7

Step  3  :

Equation at the end of step  3  :

 (((2•5x5) +  5x3) -  (2•7x2)) -  7

Step  4  :

Checking for a perfect cube :

4.1    10x5+5x3-14x2-7  is not a perfect cube

Trying to factor by pulling out :

4.2      Factoring:  10x5+5x3-14x2-7  

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

Group 1:  -14x2-7  

Group 2:  10x5+5x3  

Pull out from each group separately :

Group 1:   (2x2+1) • (-7)

Group 2:   (2x2+1) • (5x3)

Add up the two groups :

              (2x2+1)  •  (5x3-7)  

Which is the desired factorization

answer:

c. the third graph