Step-by-step explanation:
[tex] {10x}^{2} + 2 1x - 10 \\ \\ 10 {x}^{2} + 25x - 4x - 10 \\ \\ 5x(2x - 5) - 2(2x - 5) \\ \\ (5x - 2)(2x - 5)[/tex]
# be careful #STEP
1
:
Equation at the end of step 1
((2•5x2) - 21x) - 10
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 10x2-21x-10
The first term is, 10x2 its coefficient is 10 .
The middle term is, -21x its coefficient is -21 .
The last term, "the constant", is -10
Step-1 : Multiply the coefficient of the first term by the constant 10 • -10 = -100
Step-2 : Find two factors of -100 whose sum equals the coefficient of the middle term, which is -21 .
-100 + 1 = -99
-50 + 2 = -48
-25 + 4 = -21 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -25 and 4
10x2 - 25x + 4x - 10
Step-4 : Add up the first 2 terms, pulling out like factors :
5x • (2x-5)
Add up the last 2 terms, pulling out common factors :
2 • (2x-5)
Step-5 : Add up the four terms of step 4 :
(5x+2) • (2x-5)
Which is the desired factorization
Final result :
(2x - 5) • (5x + 2)
