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Mathematics
Snoopy
1 February, 09:52
Factor completely: 5x3 + 15x2 + 10x
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Kiana Benjamin
1 February, 11:34
0
-5x • (x + 2) • (x + 1)
Step-by-step explanation:
Reformatting the input:
Changes made to your input should not affect the solution:
(1) : "x2" was replaced by "x^2". 1 more similar replacement (s).
Step by step solution:
Step 1:
Equation at the end of step 1:
((0 - (5 • (x3))) - (3•5x2)) - 10x
Step 2:
Equation at the end of step 2:
((0 - 5x3) - (3•5x2)) - 10x
Step 3:
Step 4:
Pulling out like terms:
4.1 Pull out like factors:
-5x3 - 15x2 - 10x = - 5x • (x2 + 3x + 2)
Trying to factor by splitting the middle term
4.2 Factoring x2 + 3x + 2
The first term is, x2 its coefficient is 1.
The middle term is, + 3x its coefficient is 3.
The last term, "the constant", is + 2
Step-1 : Multiply the coefficient of the first term by the constant 1 • 2 = 2
Step-2 : Find two factors of 2 whose sum equals the coefficient of the middle term, which is 3.
-2 + - 1 = - 3
-1 + - 2 = - 3
1 + 2 = 3 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 1 and 2
x2 + 1x + 2x + 2
Step-4 : Add up the first 2 terms, pulling out like factors:
x • (x+1)
Add up the last 2 terms, pulling out common factors:
2 • (x+1)
Step-5 : Add up the four terms of step 4:
(x+2) • (x+1)
Which is the desired factorization
Final result:
-5x • (x + 2) • (x + 1)
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