Divide (2x^3-10x^2+x-5)÷(x-5)

$(2 x^{3} - 10 x^{2} + x - 5) \div (x - 5)$

Step 1

Rewrite the division as a fraction.

$\frac{2 x^{3} - 10 x^{2} + x - 5}{x - 5}$

Step 2

Simplify the numerator.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{(2 x^{3} - 10 x^{2}) + x - 5}{x - 5}$

Factor out the greatest common factor (GCF) from each group.

$\frac{2 x^{2} (x - 5) + 1 (x - 5)}{x - 5}$

Factor the polynomial by factoring out the greatest common factor, $x - 5$ .

$\frac{(x - 5) (2 x^{2} + 1)}{x - 5}$

Step 3

Cancel the common factor of $x - 5$ .

Cancel the common factor.

$\frac{(x - 5) (2 x^{2} + 1)}{x - 5}$

Divide $2 x^{2} + 1$ by $1$ .

$2 x^{2} + 1$