12m + 15 - 3m^2 factories
Answers
STEP
1
:
Equation at the end of step 1
(3m2 - 12m) - 15
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
3m2 - 12m - 15 = 3 • (m2 - 4m - 5)
Trying to factor by splitting the middle term
3.2 Factoring m2 - 4m - 5
The first term is, m2 its coefficient is 1 .
The middle term is, -4m its coefficient is -4 .
The last term, "the constant", is -5
Step-1 : Multiply the coefficient of the first term by the constant 1 • -5 = -5
Step-2 : Find two factors of -5 whose sum equals the coefficient of the middle term, which is -4 .
-5 + 1 = -4 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 1
m2 - 5m + 1m - 5
Step-4 : Add up the first 2 terms, pulling out like factors :
m • (m-5)
Add up the last 2 terms, pulling out common factors :
1 • (m-5)
Step-5 : Add up the four terms of step 4 :
(m+1) • (m-5)
Which is the desired factorization
Final result :
3 • (m + 1) • (m - 5)
Answer:
Simplifying
3m2 + 12m + -15 = 0
Reorder the terms:
-15 + 12m + 3m2 = 0
Solving
-15 + 12m + 3m2 = 0
Solving for variable 'm'.
Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + 4m + m2) = 0
Factor a trinomial.
3((-5 + -1m)(1 + -1m)) = 0
Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -1m)' equal to zero and attempt to solve:
Simplifying
-5 + -1m = 0
Solving
-5 + -1m = 0
Move all terms containing m to the left, all other terms to the right.
Add '5' to each side of the equation.
-5 + 5 + -1m = 0 + 5
Combine like terms: -5 + 5 = 0
0 + -1m = 0 + 5
-1m = 0 + 5
Combine like terms: 0 + 5 = 5
-1m = 5
Divide each side by '-1'.
m = -5
Simplifying
m = -5