Divide (16p^3-24p^2+8p)÷8p

$(16 p^{3} - 24 p^{2} + 8 p) \div 8 p$

Rewrite the division as a fraction.

$\frac{16 p^{3} - 24 p^{2} + 8 p}{8 p}$

Simplify the numerator.

Factor $8 p$ out of $16 p^{3} - 24 p^{2} + 8 p$ .

Factor $8 p$ out of $16 p^{3}$ .

$\frac{8 p (2 p^{2}) - 24 p^{2} + 8 p}{8 p}$

Factor $8 p$ out of $- 24 p^{2}$ .

$\frac{8 p (2 p^{2}) + 8 p (- 3 p) + 8 p}{8 p}$

Factor $8 p$ out of $8 p$ .

$\frac{8 p (2 p^{2}) + 8 p (- 3 p) + 8 p (1)}{8 p}$

Factor $8 p$ out of $8 p (2 p^{2}) + 8 p (- 3 p)$ .

$\frac{8 p (2 p^{2} - 3 p) + 8 p (1)}{8 p}$

Factor $8 p$ out of $8 p (2 p^{2} - 3 p) + 8 p (1)$ .

$\frac{8 p (2 p^{2} - 3 p + 1)}{8 p}$

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 2 \cdot 1 = 2$ and whose sum is $b = - 3$ .

Factor $- 3$ out of $- 3 p$ .

$\frac{8 p (2 p^{2} - 3 (p) + 1)}{8 p}$

Rewrite $- 3$ as $- 1$ plus $- 2$

$\frac{8 p (2 p^{2} + (- 1 - 2) p + 1)}{8 p}$

Apply the distributive property.

$\frac{8 p (2 p^{2} - 1 p - 2 p + 1)}{8 p}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{8 p ((2 p^{2} - 1 p) - 2 p + 1)}{8 p}$

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

$\frac{8 p (p (2 p - 1) - (2 p - 1))}{8 p}$

Factor the polynomial by factoring out the greatest common factor, $2 p - 1$ .

$\frac{8 p ((2 p - 1) (p - 1))}{8 p}$

$\frac{8 p (2 p - 1) (p - 1)}{8 p}$

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 p (2 p - 1) (p - 1)}{8 p}$

Rewrite the expression.

$\frac{(p (2 p - 1)) (p - 1)}{p}$

Cancel the common factor of $p$ .

Cancel the common factor.

$\frac{p (2 p - 1) (p - 1)}{p}$

Divide $(2 p - 1) (p - 1)$ by $1$ .

$(2 p - 1) (p - 1)$

Expand $(2 p - 1) (p - 1)$ using the FOIL Method.

Apply the distributive property.

$2 p (p - 1) - 1 (p - 1)$

Apply the distributive property.

$2 p \cdot p + 2 p \cdot - 1 - 1 (p - 1)$

Apply the distributive property.

$2 p \cdot p + 2 p \cdot - 1 - 1 p - 1 \cdot - 1$

Simplify and combine like terms.

Simplify each term.

Multiply $p$ by $p$ by adding the exponents.

Move $p$ .

$2 (p \cdot p) + 2 p \cdot - 1 - 1 p - 1 \cdot - 1$

Multiply $p$ by $p$ .

$2 p^{2} + 2 p \cdot - 1 - 1 p - 1 \cdot - 1$

Multiply $- 1$ by $2$ .

$2 p^{2} - 2 p - 1 p - 1 \cdot - 1$

Rewrite $- 1 p$ as $- p$ .

$2 p^{2} - 2 p - p - 1 \cdot - 1$

Multiply $- 1$ by $- 1$ .

$2 p^{2} - 2 p - p + 1$

Subtract $p$ from $- 2 p$ .

$2 p^{2} - 3 p + 1$

Divide (16p^3-24p^2+8p)÷8p

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