Question

Find (x4 - 5x3 + 17x + 3) divided by (x – 3).

Answer 1

First we make x-3=0 and solve for x, that is x=3. Then we write the polynomial with all the monomials (including those that have null coefficient)

$x^4-5x^3+0x^2+17x+3$

and we take over the coefficients, 1, -5, 0, 17, 3. So we start with our method

Now, we take all the new coefficient and low the grade of the polynomial, the new coefficients are 1, -2, -6, -1, 0, so

$1x^3-2x^2-6x-1+\frac{0}{x-3}$

Since the remainder is zero, we can take it off, so x^4-5x^3+17x+3 divided by x-3 is equal to

$x^3-2x^2-6x-1$