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Use the long division method to find the result when 2, x, cubed, plus, 5, x, squared, minus, 20, x, plus, 42x

3
+5x
2
−20x+4 is divided by x, minus, 2x−2.

Solve the problem just like the example below
⬇️
Use the long division method to find the result when
4, x, cubed, plus, 12, x, squared, plus, 27, x, plus, 27
4x
3
+12x
2
+27x+27 is divided by
2, x, plus, 3
2x+3.
Use Long Division:
Use Long Division:

2, x, squared
2x
2
plus, 3, x
+3x
plus, 9
+9

2, x
2x
plus, 3
+3
right parenthesis
)
4, x, cubed
4x
3
plus, 12, x, squared
+12x
2
plus, 27, x
+27x
plus, 27
+27

start superscript, minus, end superscript, 4, x, cubed
−
4x
3
plus, start superscript, minus, end superscript, 6, x, squared
+
−
6x
2

6, x, squared
6x
2
plus, 27, x
+27x
plus, 27
+27

start superscript, minus, end superscript, 6, x, squared
−
6x
2
plus, start superscript, minus, end superscript, 9, x
+
−
9x

18, x
18x
plus, 27
+27

start superscript, minus, end superscript, 18, x
−
18x
plus, start superscript, minus, end superscript, 27
+
−
27

0
0

Answer: , 2, x, squared, plus, 3, x, plus, 9
Answer: 2x
2
+3x+9

1 answer

Let's find the result when \( 2x^3 + 5x^2 - 20x + 42 \) is divided by \( x - 2 \) using long division.

Use Long Division:

                   2x^2 + 9x + -12   
                ________________________
x - 2     |  2x^3 + 5x^2 - 20x + 42
  1. First Step:
    • Divide the first term: \( 2x^3 \div x = 2x^2 \).
    • Multiply: \( 2x^2(x - 2) = 2x^3 - 4x^2 \).
    • Subtract:
                      2x^2
                ________________________
x - 2     |  2x^3 + 5x^2 - 20x + 42
          - (2x^3 - 4x^2)
          ________________________
                     9x^2 - 20x + 42
  1. Second Step:
    • Divide the first term: \( 9x^2 \div x = 9x \).
    • Multiply: \( 9x(x - 2) = 9x^2 - 18x \).
    • Subtract:
                      2x^2 + 9x
                ________________________
x - 2     |  2x^3 + 5x^2 - 20x + 42
          - (2x^3 - 4x^2)
          ________________________
                     9x^2 - 20x + 42
         - (9x^2 - 18x)
          ________________________
                          -2x + 42
  1. Third Step:
    • Divide the first term: \( -2x \div x = -2 \).
    • Multiply: \( -2(x - 2) = -2x + 4 \).
    • Subtract:
                      2x^2 + 9x - 2
                ________________________
x - 2     |  2x^3 + 5x^2 - 20x + 42
          - (2x^3 - 4x^2)
          ________________________
                     9x^2 - 20x + 42
         - (9x^2 - 18x)
          ________________________
                          -2x + 42
                     - (-2x + 4)
          ________________________
                                  38

Final Answer:

The result of dividing \( 2x^3 + 5x^2 - 20x + 42 \) by \( x - 2 \) is \[ 2x^2 + 9x - 2 \quad \text{with a remainder} \quad 38. \]

So the final answer is: \[ \text{Answer: } 2x^2 + 9x - 2 \quad \text{Remainder: } 38. \]