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