Question

Factor:
2m² + 3m - 9

Answer 1

(2m-3) * (m+3)

Explanation:

Step-1 : Multiply the coefficient of the first term by the constant 2 • -9 = -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

-3 + 6 = 3 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 6

2m2 - 3m + 6m - 9

Step-4 : Add up the first 2 terms, pulling out like factors :

m • (2m-3)

Add up the last 2 terms, pulling out common factors :

3 • (2m-3)

Step-5 : Add up the four terms of step 4 :

(m+3) • (2m-3)

Which is the desired factorization

Final result :

(2m - 3) • (m + 3)

Answer 2

2m2+3m-9

Final result :

(2m - 3) • (m + 3)
Reformatting the input :

Changes made to your input should not affect the solution:

(1): "m2" was replaced by "m^2".

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(2m2 + 3m) - 9
Step 2 :

Trying to factor by splitting the middle term

2.1 Factoring 2m2+3m-9

The first term is, 2m2 its coefficient is 2 .
The middle term is, +3m its coefficient is 3 .
The last term, "the constant", is -9

Step-1 : Multiply the coefficient of the first term by the constant 2 • -9 = -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
-3 + 6 = 3 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 6
2m2 - 3m + 6m - 9

Step-4 : Add up the first 2 terms, pulling out like factors :
m • (2m-3)
Add up the last 2 terms, pulling out common factors :
3 • (2m-3)
Step-5 : Add up the four terms of step 4 :
(m+3) • (2m-3)
Which is the desired factorization

Final result :

(2m - 3) • (m + 3)