How do you find the quotient of (5x^3 - 14x + 3) by x -2?

You have the option to divide the remainder by 15.

I've made an effort to arrange the divide:

5x³    -14x+3 ∣ x-2 5x³-10x²                                         +10x+6                                                      à

To find the quotient of (5x^3 - 14x + 3) divided by (x - 2), you can use polynomial long division.

First, divide the first term of the dividend (5x^3) by the first term of the divisor (x), which gives you 5x^2. Multiply this result by the entire divisor (x - 2), giving you 5x^2(x - 2) = 5x^3 - 10x^2.

Next, subtract this result from the original dividend: (5x^3 - 14x + 3) - (5x^3 - 10x^2) = -10x^2 - 14x + 3.

Now, repeat the process with the new polynomial (-10x^2 - 14x + 3) as the dividend. Divide the first term (-10x^2) by the first term (x) of the divisor, resulting in -10x. Multiply this by the entire divisor (x - 2), giving you -10x(x - 2) = -10x^2 + 20x.

Subtract this result from the current dividend: (-10x^2 - 14x + 3) - (-10x^2 + 20x) = -34x + 3.

Since the degree of the new polynomial (-34x + 3) is less than the degree of the divisor (x - 2), we have reached the end of the division.

Therefore, the quotient of (5x^3 - 14x + 3) divided by (x - 2) is 5x^2 - 10x - 34 with a remainder of 3.