A student performed the following steps to find the solution to the equation x2 + 4x -12=0 Where did the student go wrong?
Step 1. Factor the polynomial into (x+6) and (x-2)
Step 2. X-6 = 0 and x + 2 = 0
Step 3. x = 6 and x = -2
A. in Step 2
B. in Step 1
C. in Step 3
D. The student did not make any mistakes, the solution is correct

Step 2.

Step-by-step explanation:

Step 2. In step 1, they correctly wrote the factors of the polynomial as (x+6) and (x-2). But then in step 2, (x+6) suddenly became (x-6) and (x-2) became (x+2), which is incorrect.

The answers in step 3 should have been -6 and  2.

1. 8

2. 9

3. 20

4. 3

5. 17

6. 2.2

7. 11.25

8. 1

9. 14

10. 2

step-by-step explanation:

thats the first half

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!