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