Question

find the solution of 6+x-x^2>0

Answer 1

6-x-x2>gt;0

Step by step solution :

Step 1 :

Step 2 :

Pulling out like terms :

2.1 Pull out like factors :

-x2 - x + 6 = -1 • (x2 + x - 6)

Trying to factor by splitting the middle term

2.2 Factoring x2 + x - 6

The first term is, x2 its coefficient is 1 .

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 1 • -6 = -6

Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is 1 .

-6 + 1 = -5

-3 + 2 = -1

-2 + 3 = 1 That's it

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

x2 - 2x + 3x - 6

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

x • (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 :

(x+3) • (x-2)

Which is the desired factorization

Equation at the end of step 2 :

(-x - 3) • (x - 2) > 0

Answer 2

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