Write in Standard Form P(x)=x^3(-3x+x^2+7)

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

Step 1

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

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

Step 2

Apply the distributive property.

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

Step 3

Simplify.

Rewrite using the commutative property of multiplication.

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

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

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

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

Add $3$ and $2$ .

$P (x) = - 3 x^{3} x + x^{5} + x^{3} \cdot 7$

Move $7$ to the left of $x^{3}$ .

$P (x) = - 3 x^{3} x + x^{5} + 7 \cdot x^{3}$

Step 4

Multiply $x^{3}$ by $x$ by adding the exponents.

Move $x$ .

$P (x) = - 3 (x \cdot x^{3}) + x^{5} + 7 \cdot x^{3}$

Multiply $x$ by $x^{3}$ .

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

$P (x) = - 3 (x \cdot x^{3}) + x^{5} + 7 \cdot x^{3}$

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

$P (x) = - 3 x^{1 + 3} + x^{5} + 7 \cdot x^{3}$

Add $1$ and $3$ .

$P (x) = - 3 x^{4} + x^{5} + 7 \cdot x^{3}$

$P (x) = - 3 x^{4} + x^{5} + 7 x^{3}$

Step 5

Reorder $- 3 x^{4}$ and $x^{5}$ .

$P (x) = x^{5} - 3 x^{4} + 7 x^{3}$