Question

middle split the equation 2x^2+14x+58

Answer 1

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

(2x2 - 14x) - 240 = 0

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

2x2 - 14x - 240 = 2 • (x2 - 7x - 120)

Trying to factor by splitting the middle term

3.2 Factoring x2 - 7x - 120

The first term is, x2 its coefficient is 1 .

The middle term is, -7x its coefficient is -7 .

The last term, "the constant", is -120

Step-1 : Multiply the coefficient of the first term by the constant 1 • -120 = -120

Step-2 : Find two factors of -120 whose sum equals the coefficient of the middle term, which is -7 .

-120 + 1 = -119

-60 + 2 = -58

-40 + 3 = -37

-30 + 4 = -26

-24 + 5 = -19

-20 + 6 = -14

-15 + 8 = -7 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and 8

x2 - 15x + 8x - 120

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

x • (x-15)

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

8 • (x-15)

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

(x+8) • (x-15)

Which is the desired factorization

Equation at the end of step

3

: