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

Answer: (3✖️ - 7) (9✖️ + 2)

Step-by-step explanation:

3^3 ✖️^2 - 57✖️) - 14

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)