First, we divide the leading term of the numerator by the leading term of the denominator8x^3 ÷ 4x^2 = 2x
Next, we multiply the entire denominator by 2x2x(4x^2 - 2x + 1) = 8x^3 - 4x^2 + 2x
Subtract this result from the numerator8x^3 + 12x^2 - 6x + 4 - (8x^3 - 4x^2 + 2x) = 16x^2 - 8x + 4
Now, we continue the division process by repeating the steps above with the new result 16x^2 - 8x + 4 as the new numerator.
First, we divide the leading term of the numerator by the leading term of the denominatorx^4 ÷ x = x^3
Next, we multiply the entire denominator by x^3x^3(x + 2) = x^4 + 2x^3
Subtract this result from the numeratorx^4 + x^2 - 4 + 2x^3 - (x^4 + 2x^3) = x^2 - 4
Now, we continue the division process by repeating the steps above with the new result x^2 - 4 as the new numerator.
First, we divide the leading term of the numerator by the leading term of the denominator
8x^3 ÷ 4x^2 = 2x
Next, we multiply the entire denominator by 2x
2x(4x^2 - 2x + 1) = 8x^3 - 4x^2 + 2x
Subtract this result from the numerator
8x^3 + 12x^2 - 6x + 4 - (8x^3 - 4x^2 + 2x) = 16x^2 - 8x + 4
Now, we continue the division process by repeating the steps above with the new result 16x^2 - 8x + 4 as the new numerator.
(x^4 + x^2 - 4 + 2x^3) ÷ (x + 2)First, we divide the leading term of the numerator by the leading term of the denominator
x^4 ÷ x = x^3
Next, we multiply the entire denominator by x^3
x^3(x + 2) = x^4 + 2x^3
Subtract this result from the numerator
x^4 + x^2 - 4 + 2x^3 - (x^4 + 2x^3) = x^2 - 4
Now, we continue the division process by repeating the steps above with the new result x^2 - 4 as the new numerator.