-5u2+15u+90
Final result :
-5 • (u + 3) • (u - 6)
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((0 - 5u2) + 15u) + 90
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
-5u2 + 15u + 90 = -5 • (u2 - 3u - 18)
Trying to factor by splitting the middle term
3.2 Factoring u2 - 3u - 18
The first term is, u2 its coefficient is 1 .
The middle term is, -3u its coefficient is -3 .
The last term, "the constant", is -18
Step-1 : Multiply the coefficient of the first term by the constant 1 • -18 = -18
Step-2 : Find two factors of -18 whose sum equals the coefficient of the middle term, which is -3 .
-18
+
1
=
-17
-9
+
2
=
-7
-6
+
3
=
-3
That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 3
u2 - 6u + 3u - 18
Step-4 : Add up the first 2 terms, pulling out like factors :
u • (u-6)
Add up the last 2 terms, pulling out common factors :
3 • (u-6)
Step-5 : Add up the four terms of step 4 :
(u+3) • (u-6)
Which is the desired factorization
Final result :
-5 • (u + 3) • (u - 6)
