Question

The expression shown represents a function: x^2+4x-12
For what positive value of x will the graph of the function cross the x-axis?
For what negative value of x will the graph of the function cross the x-axis?

Answer 1

Step by step solution :
Step 1 :

Simplify x2+4x - 12

Trying to factor by splitting the middle term

1.1 Factoring x^2+4x-12

The first term is, x^2 its coefficient is 1 .
The middle term is, +4x its coefficient is 4 .
The last term, "the constant", is -12

Step-1 : Multiply the coefficient of the first term by the constant 1 • -12 = -12

Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is 4 .
-12 + 1 = -11
-6 + 2 = -4
-4 + 3 = -1
-3 + 4 = 1
-2 + 6 = 4 That's it


Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 6
x^2 - 2x + 6x - 12

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 :
6 • (x-2)
Now add up the four terms of step 3 :
(x+6) • (x-2)
Which is the desired factorization
Final result :

(x + 6) • (x - 2)

Answer 2

My sheet says the answer must be a single, regular number like: 2, 6, -5, etc. Would I multiply 6 and -2?

Answer 3

yes

Answer 4

So, is 6 the positive answer and -12 the negative answer?

Answer 5

I mean -2

Answer 6

yeah