Use the long division method to find the result when 3, x, cubed, plus, 10, x, squared, plus, 15, x, plus, 143x

Question

3
+10x
2
+15x+14 is divided by x, plus, 2x+2.

Solve the problem just like the example below
⬇️
Use the long division method to find the result when
4, x, cubed, plus, 5, x, squared, plus, 5, x, plus, 1
4x
3
+5x
2
+5x+1 is divided by
4, x, plus, 1
4x+1.
Use Long Division:
Use Long Division:

x, squared
x
2
plus, x
+x
plus, 1
+1

4, x
4x
plus, 1
+1
right parenthesis
)
4, x, cubed
4x
3
plus, 5, x, squared
+5x
2
plus, 5, x
+5x
plus, 1
+1

start superscript, minus, end superscript, 4, x, cubed
−
4x
3
plus, start superscript, minus, end superscript, x, squared
+
−
x
2

4, x, squared
4x
2
plus, 5, x
+5x
plus, 1
+1

start superscript, minus, end superscript, 4, x, squared
−
4x
2
plus, start superscript, minus, end superscript, x
+
−
x

4, x
4x
plus, 1
+1

start superscript, minus, end superscript, 4, x
−
4x
plus, start superscript, minus, end superscript, 1
+
−
1

0
0

Answer: , x, squared, plus, x, plus, 1
Answer: x
2
+x+1

Answer 1

To find the result of dividing \( 3x^3 + 10x^2 + 15x + 14 \) by \( x + 2 \) using the long division method, we will follow the same steps demonstrated in your example.

Use Long Division:

1. Set up the Division: \[ \begin{array}{r|l} & x + 2 \ \hline & 3x^3 + 10x^2 + 15x + 14 \ \end{array} \]

2. Divide the first term:

   • Divide \( 3x^3 \) by \( x \) to get \( 3x^2 \).

3. Multiply and subtract:

   • Multiply \( 3x^2 \) by \( (x + 2) \): \[ 3x^2(x + 2) = 3x^3 + 6x^2 \]
   • Now subtract: \[ \begin{array}{r|l} & x + 2 \ \hline & 3x^3 + 10x^2 + 15x + 14 \
   • & (3x^3 + 6x^2) \ \hline & 0 + 4x^2 + 15x + 14 \ \end{array} \]

4. Divide the next term:

   • Now divide \( 4x^2 \) by \( x \) to get \( 4x \).

5. Multiply and subtract again:

   • Multiply \( 4x \) by \( (x + 2) \): \[ 4x(x + 2) = 4x^2 + 8x \]
   • Now subtract: \[ \begin{array}{r|l} & x + 2 \ \hline & 4x^2 + 15x + 14 \
   • & (4x^2 + 8x) \ \hline & 0 + 7x + 14 \ \end{array} \]

6. Divide the next term:

   • Now divide \( 7x \) by \( x \) to get \( 7 \).

7. Multiply and subtract again:

   • Multiply \( 7 \) by \( (x + 2) \): \[ 7(x + 2) = 7x + 14 \]
   • Now subtract: \[ \begin{array}{r|l} & x + 2 \ \hline & 7x + 14 \
   • & (7x + 14) \ \hline & 0 \ \end{array} \]

Final Result

Since we have reached a remainder of 0, the division is complete. Combining our results, we have:

\[ 3x^3 + 10x^2 + 15x + 14 \div (x + 2) = 3x^2 + 4x + 7 \]

Answer: \( 3x^2 + 4x + 7 \)