Question

Using synthetic division, what is the quotient: (3x3 + 4x - 32) ÷ (x - 2)

Answer 1

Solve for x:
3 x^2+6 x+16 = 0
Write the quadratic equation in standard form.
Divide both sides by 3:
x^2+2 x+16/3 = 0
Solve the quadratic equation by completing the square.
Subtract 16/3 from both sides:
x^2+2 x = -16/3
Take one half of the coefficient of x and square it, then add it to both sides.
Add 1 to both sides:
x^2+2 x+1 = -13/3
Factor the left hand side.
Write the left hand side as a square:
(x+1)^2 = -13/3
Eliminate the exponent on the left hand side.
Take the square root of both sides:
x+1 = i sqrt(13/3) or x+1 = -i sqrt(13/3)
Look at the first equation: Solve for x.
Subtract 1 from both sides:
x = i sqrt(13/3)-1 or x+1 = -i sqrt(13/3)
Look at the second equation: Solve for x.
Subtract 1 from both sides:
Answer: |
| x = i sqrt(13/3)-1 or x = -i sqrt(13/3)-1