Question

(3х3+12х2-51х-180):(х+3)=

Answer 1

Відповідь:     3х² + 3х - 60 .

Пояснення:

     ( 3х³ + 12х²- 51х - 180 ) : ( х + 3 ) = 3х² + 3х - 60 .

  # Краще ділення виконати " кутом " ( як ділення многоцифрових

     чисел )  або  за формулою Безу .

Answer 2

Ответ:           3x^2+3x-60.

Объяснение:

(3х^3+12х^2-51х-180):(х+3)=3x^2+3x-60.

(См. скриншот)

Answer 3

To simplify the expression $\frac{3x^3 + 12x^2 - 51x - 180}{x + 3}$, you can perform polynomial long division. Here's how you can do it step by step:

1. Divide the first term of the numerator by the first term of the denominator:

$$\begin{align*} \frac{3x^3}{x} &= 3x^2 \end{align*}$$

2. Multiply the denominator ($x + 3$) by the result from step 1 ($3x^2$) and subtract it from the numerator:

$$\begin{align*} 3x^2(x + 3) &= 3x^3 + 9x^2 \\ (3x^3 + 12x^2 - 51x - 180) - (3x^3 + 9x^2) &= (12x^2 - 51x - 180) - (9x^2) \end{align*}$$

3. Now, we have $12x^2 - 51x - 180$ in the numerator. Repeat the process:

   a. Divide the first term of the new numerator ($12x^2$) by the first term of the denominator ($x$):

$$\begin{align*} \frac{12x^2}{x} &= 12x \end{align*}$$

b. Multiply the denominator ($x + 3$) by the result from step 3a ($12x$) and subtract it from the new numerator:

$$\begin{align*} 12x(x + 3) &= 12x^2 + 36x \\ (12x^2 - 51x - 180) - (12x^2 + 36x) &= (-51x - 180) - (36x) \end{align*}$$

4. Now, we have $-51x - 180$ in the numerator. Repeat the process:

   a. Divide the first term of the new numerator ($-51x$) by the first term of the denominator ($x$):

$$\begin{align*} \frac{-51x}{x} &= -51 \end{align*}$$

b. Multiply the denominator ($x + 3$) by the result from step 4a ($-51$) and subtract it from the new numerator:

$$\begin{align*} -51(x + 3) &= -51x - 153 \\ (-51x - 180) - (-51x - 153) &= (-51x - 180) + (51x + 153) \end{align*}$$

5. Now, we have $-51x - 180 + 51x + 153$ in the numerator:

$$\begin{align*} (-51x - 180) + (51x + 153) &= -27 \end{align*}$$

So, the simplified expression is $-27$.