Write in Standard Form f(x)=(3x+1)(x+2)(x-3)

$f (x) = (3 x + 1) (x + 2) (x - 3)$

Step 1

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

$f (x) = a x^{2} + b x + c$

Step 2

Expand $(3 x + 1) (x + 2)$ using the FOIL Method.

Apply the distributive property.

$f (x) = (3 x (x + 2) + 1 (x + 2)) (x - 3)$

Apply the distributive property.

$f (x) = (3 x \cdot x + 3 x \cdot 2 + 1 (x + 2)) (x - 3)$

Apply the distributive property.

$f (x) = (3 x \cdot x + 3 x \cdot 2 + 1 x + 1 \cdot 2) (x - 3)$

Step 3

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$f (x) = (3 (x \cdot x) + 3 x \cdot 2 + 1 x + 1 \cdot 2) (x - 3)$

Multiply $x$ by $x$ .

$f (x) = (3 x^{2} + 3 x \cdot 2 + 1 x + 1 \cdot 2) (x - 3)$

Multiply $2$ by $3$ .

$f (x) = (3 x^{2} + 6 x + 1 x + 1 \cdot 2) (x - 3)$

Multiply $x$ by $1$ .

$f (x) = (3 x^{2} + 6 x + x + 1 \cdot 2) (x - 3)$

Multiply $2$ by $1$ .

$f (x) = (3 x^{2} + 6 x + x + 2) (x - 3)$

Add $6 x$ and $x$ .

$f (x) = (3 x^{2} + 7 x + 2) (x - 3)$

Step 4

Expand $(3 x^{2} + 7 x + 2) (x - 3)$ by multiplying each term in the first expression by each term in the second expression.

$f (x) = 3 x^{2} x + 3 x^{2} \cdot - 3 + 7 x \cdot x + 7 x \cdot - 3 + 2 x + 2 \cdot - 3$

Step 5

Simplify terms.

Simplify each term.

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$f (x) = 3 (x \cdot x^{2}) + 3 x^{2} \cdot - 3 + 7 x \cdot x + 7 x \cdot - 3 + 2 x + 2 \cdot - 3$

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$f (x) = 3 (x \cdot x^{2}) + 3 x^{2} \cdot - 3 + 7 x \cdot x + 7 x \cdot - 3 + 2 x + 2 \cdot - 3$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f (x) = 3 x^{1 + 2} + 3 x^{2} \cdot - 3 + 7 x \cdot x + 7 x \cdot - 3 + 2 x + 2 \cdot - 3$

Add $1$ and $2$ .

$f (x) = 3 x^{3} + 3 x^{2} \cdot - 3 + 7 x \cdot x + 7 x \cdot - 3 + 2 x + 2 \cdot - 3$

Multiply $- 3$ by $3$ .

$f (x) = 3 x^{3} - 9 x^{2} + 7 x \cdot x + 7 x \cdot - 3 + 2 x + 2 \cdot - 3$

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

Move $x$ .

$f (x) = 3 x^{3} - 9 x^{2} + 7 (x \cdot x) + 7 x \cdot - 3 + 2 x + 2 \cdot - 3$

Multiply $x$ by $x$ .

$f (x) = 3 x^{3} - 9 x^{2} + 7 x^{2} + 7 x \cdot - 3 + 2 x + 2 \cdot - 3$

Multiply $- 3$ by $7$ .

$f (x) = 3 x^{3} - 9 x^{2} + 7 x^{2} - 21 x + 2 x + 2 \cdot - 3$

Multiply $2$ by $- 3$ .

$f (x) = 3 x^{3} - 9 x^{2} + 7 x^{2} - 21 x + 2 x - 6$

Simplify by adding terms.

Add $- 9 x^{2}$ and $7 x^{2}$ .

$f (x) = 3 x^{3} - 2 x^{2} - 21 x + 2 x - 6$

Add $- 21 x$ and $2 x$ .

$f (x) = 3 x^{3} - 2 x^{2} - 19 x - 6$

Write in Standard Form f(x)=(3x+1)(x+2)(x-3)

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