15x2+25x−10
Factorize
Answers
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((3•5x2) - 25x) - 10
Pulling out like terms :
3.1 Pull out like factors :
15x2 - 25x - 10 = 5 • (3x2 - 5x - 2)
Trying to factor by splitting the middle term
3.2 Factoring 3x2 - 5x - 2
The first term is, 3x2 its coefficient is 3 .
The middle term is, -5x its coefficient is -5 .
The last term, "the constant", is -2
Step-1 : Multiply the coefficient of the first term by the constant 3 • -2 = -6
Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is -5 .
-6 + 1 = -5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 1
3x2 - 6x + 1x - 2
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (x-2)
Add up the last 2 terms, pulling out common factors :
1 • (x-2)
Step-5 : Add up the four terms of step 4 :
(3x+1) • (x-2)
Which is the desired factorization
Final result :
5 • (x - 2) • (3x + 1)
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