Write in Standard Form (3+x)(2x-5)

$(3 + x) (2 x - 5)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Expand $(3 + x) (2 x - 5)$ using the FOIL Method.

Apply the distributive property.

$3 (2 x - 5) + x (2 x - 5)$

Apply the distributive property.

$3 (2 x) + 3 \cdot - 5 + x (2 x - 5)$

Apply the distributive property.

$3 (2 x) + 3 \cdot - 5 + x (2 x) + x \cdot - 5$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $3$ .

$6 x + 3 \cdot - 5 + x (2 x) + x \cdot - 5$

Multiply $3$ by $- 5$ .

$6 x - 15 + x (2 x) + x \cdot - 5$

Rewrite using the commutative property of multiplication.

$6 x - 15 + 2 x \cdot x + x \cdot - 5$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$6 x - 15 + 2 (x \cdot x) + x \cdot - 5$

Multiply $x$ by $x$ .

$6 x - 15 + 2 x^{2} + x \cdot - 5$

Move $- 5$ to the left of $x$ .

$6 x - 15 + 2 x^{2} - 5 x$

Subtract $5 x$ from $6 x$ .

$x - 15 + 2 x^{2}$

Step 4

Move $- 15$ .

$x + 2 x^{2} - 15$

Step 5

Reorder $x$ and $2 x^{2}$ .

$2 x^{2} + x - 15$