Question

1. Solve for x
x^2+5x+16=-3x+4

2.Solve for x
2x^2+2x-11=3x-5

3.Factor 8x^3-y3

4.Factor 24x^3+81y^3

Please explain how you got answer and 1 question each person, so that everyone can get a medal for answering.

Answer 1

1. X=-6, x=-2

Answer 2

Your equation is:
x^2+5x+16 = -3x+4
Simplified form is:
x^2 + 8x + 12 = 0
The solutions of this equation are:
X1 = -2
X2 = -6

Answer 3

2. Your equation is:
2x^2+2x-11 = 3x-5
Simplified form is:
2x^2 - x - 6 = 0
The solutions of this equation are:
X1 = 2
X2 = -3/2

Answer 4

4. Result
24x3+81y3=3(2x+3y)(4x2−6xy+9y2)
Explanation
Step 1 :
After factoring out 3 we have:
24x3+81y3=3(8x3+27y3)
Step 2 :
To factor 8x3+27y3 we can use sum of cubes formula:
I3+II3=(I+II)(I2−I⋅II+II2)
After putting I=2x and II=3y , we have:
8x3+27y3=(2x+3y)(4x2−6xy+9y2)

Answer 5

3. Result
8x3−y3=(2x−y)(4x2+2xy+y2)
Explanation
To factor 8x3−y3 we can use difference of cubes formula:
I3−II3=(I−II)(I2+I⋅II+II2)
After putting I=2x and II=y , we have:
8x3−y3=(2x−y)(4x2+2xy+y2)

Answer 6

Thankyou :)

Answer 7

I thought I should only have 1 x