How is 27x^2-57x+14 factored

27x2-57x-14

Final result :

(3x - 7) • (9x + 2)
Step by step solution :

Step 1 :

Equation at the end of step 1 :

(33x2 - 57x) - 14
Step 2 :

Trying to factor by splitting the middle term

2.1 Factoring 27x2-57x-14

The first term is, 27x2 its coefficient is 27 .
The middle term is, -57x its coefficient is -57 .
The last term, "the constant", is -14

Step-1 : Multiply the coefficient of the first term by the constant 27 • -14 = -378

Step-2 : Find two factors of -378 whose sum equals the coefficient of the middle term, which is -57 .

-378 + 1 = -377
-189 + 2 = -187
-126 + 3 = -123
-63 + 6 = -57 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -63 and 6
27x2 - 63x + 6x - 14

Step-4 : Add up the first 2 terms, pulling out like factors :
9x • (3x-7)
Add up the last 2 terms, pulling out common factors :
2 • (3x-7)
Step-5 : Add up the four terms of step 4 :
(9x+2) • (3x-7)
Which is the desired factorization

Final result :

(3x - 7) • (9x + 2)

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