Solve P(x) = - (x + 3) * (x + 1)(x - 3)(x - 4) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$P(x)=-(x+3)(x+1)(x-3)(x-4)$$

Evaluate

$-\left(x-4\right)\left(x+1\right)\left(x^{2}-9\right)$

Solution Steps

To find the opposite of $x+3$, find the opposite of each term.

$$\left(-x-3\right)\left(x+1\right)\left(x-3\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of $-x-3$ by each term of $x+1$.

$$\left(-x^{2}-x-3x-3\right)\left(x-3\right)\left(x-4\right)$$

Combine $-x$ and $-3x$ to get $-4x$.

$$\left(-x^{2}-4x-3\right)\left(x-3\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of $-x^{2}-4x-3$ by each term of $x-3$.

$$\left(-x^{3}+3x^{2}-4x^{2}+12x-3x+9\right)\left(x-4\right)$$

Combine $3x^{2}$ and $-4x^{2}$ to get $-x^{2}$.

$$\left(-x^{3}-x^{2}+12x-3x+9\right)\left(x-4\right)$$

Combine $12x$ and $-3x$ to get $9x$.

$$\left(-x^{3}-x^{2}+9x+9\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of $-x^{3}-x^{2}+9x+9$ by each term of $x-4$.

$$-x^{4}+4x^{3}-x^{3}+4x^{2}+9x^{2}-36x+9x-36$$

Combine $4x^{3}$ and $-x^{3}$ to get $3x^{3}$.

$$-x^{4}+3x^{3}+4x^{2}+9x^{2}-36x+9x-36$$

Combine $4x^{2}$ and $9x^{2}$ to get $13x^{2}$.

$$-x^{4}+3x^{3}+13x^{2}-36x+9x-36$$

Combine $-36x$ and $9x$ to get $-27x$.

$$-x^{4}+3x^{3}+13x^{2}-27x-36$$

Expand

$-\left(x^{4}-3x^{3}-13x^{2}+27x+36\right)$

Solution Steps

To find the opposite of $x+3$, find the opposite of each term.

$$\left(-x-3\right)\left(x+1\right)\left(x-3\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of $-x-3$ by each term of $x+1$.

$$\left(-x^{2}-x-3x-3\right)\left(x-3\right)\left(x-4\right)$$

Combine $-x$ and $-3x$ to get $-4x$.

$$\left(-x^{2}-4x-3\right)\left(x-3\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of $-x^{2}-4x-3$ by each term of $x-3$.

$$\left(-x^{3}+3x^{2}-4x^{2}+12x-3x+9\right)\left(x-4\right)$$

Combine $3x^{2}$ and $-4x^{2}$ to get $-x^{2}$.

$$\left(-x^{3}-x^{2}+12x-3x+9\right)\left(x-4\right)$$

Combine $12x$ and $-3x$ to get $9x$.

$$\left(-x^{3}-x^{2}+9x+9\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of $-x^{3}-x^{2}+9x+9$ by each term of $x-4$.

$$-x^{4}+4x^{3}-x^{3}+4x^{2}+9x^{2}-36x+9x-36$$

Combine $4x^{3}$ and $-x^{3}$ to get $3x^{3}$.

$$-x^{4}+3x^{3}+4x^{2}+9x^{2}-36x+9x-36$$

Combine $4x^{2}$ and $9x^{2}$ to get $13x^{2}$.

$$-x^{4}+3x^{3}+13x^{2}-36x+9x-36$$

Combine $-36x$ and $9x$ to get $-27x$.

$$-x^{4}+3x^{3}+13x^{2}-27x-36$$