Answer:
Explanation:
STEP
1
:
Equation at the end of step 1
STEP
2
:
Equation at the end of step
2
:
STEP
3
:
2x3 - x2 - 6x
Simplify —————————————
2x2 - 7x + 6
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
2x3 - x2 - 6x = x • (2x2 - x - 6)
Trying to factor by splitting the middle term
4.2 Factoring 2x2 - x - 6
The first term is, 2x2 its coefficient is 2 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -6
Step-1 : Multiply the coefficient of the first term by the constant 2 • -6 = -12
Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is -1 .
-12 + 1 = -11
-6 + 2 = -4
-4 + 3 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 3
2x2 - 4x + 3x - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (x-2)
Add up the last 2 terms, pulling out common factors :
3 • (x-2)
Step-5 : Add up the four terms of step 4 :
(2x+3) • (x-2)
Which is the desired factorization
Trying to factor by splitting the middle term
4.3 Factoring 2x2-7x+6
The first term is, 2x2 its coefficient is 2 .
The middle term is, -7x its coefficient is -7 .
The last term, "the constant", is +6
Step-1 : Multiply the coefficient of the first term by the constant 2 • 6 = 12
Step-2 : Find two factors of 12 whose sum equals the coefficient of the middle term, which is -7 .
-12 + -1 = -13
-6 + -2 = -8
-4 + -3 = -7 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and -3
2x2 - 4x - 3x - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (x-2)
Add up the last 2 terms, pulling out common factors :
3 • (x-2)
Step-5 : Add up the four terms of step 4 :
(2x-3) • (x-2)
Which is the desired factorization
Canceling Out :
4.4 Cancel out (x-2) which appears on both sides of the fraction line.
Final result :
x • (2x + 3)
————————————
2x - 3