Divide 2x^3-7x^2+2x+3 by x-3 using long divison
To divide 2x^3 - 7x^2 + 2x + 3 by x - 3 using long division, follow these steps:
Step 1: Write the division problem in long division format:
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x - 3 | 2x^3 - 7x^2 + 2x + 3
Step 2: Divide the first term of the dividend (2x^3) by the first term of the divisor (x), which gives you 2x^2.
Write this quotient above the division line.
2x^2
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x - 3 | 2x^3 - 7x^2 + 2x + 3
Step 3: Multiply the divisor (x - 3) by the quotient (2x^2), and write the result below the dividend, aligning the like terms.
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x - 3 | 2x^3- 7x^2 + 2x + 3
- (2x^3 - 6x^2)
-x^2 + 2x
Step 4: Bring down the next term from the dividend, which is 2x, and write it next to the result obtained after subtracting.
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x - 3 | 2x^3- 7x^2 + 2x + 3
- (2x^3 - 6x^2)
-x^2 + 2x
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2x + 3
Step 5: Divide the first term of the new dividend (2x) by the first term of the divisor (x), which gives you 2.
Write this quotient above the division line.
2x^2 + 2
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x - 3 | 2x^3- 7x^2 + 2x + 3
- (2x^3 - 6x^2)
-x^2 + 2x
___________
2x + 3
Step 6: Multiply the divisor (x - 3) by the new quotient (2x + 2), and write the result below the previous result.
2x^2 + 2
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x - 3 | 2x^3- 7x^2 + 2x + 3
- (2x^3 - 6x^2)
-x^2 + 2x
___________
2x + 3
- (2x^2 - 6x)
8x + 3
Step 7: There are no more terms to bring down. The remainder is 8x + 3.
Therefore, the quotient of 2x^3 - 7x^2 + 2x + 3 divided by x - 3 is 2x^2 + 2 with a remainder of 8x + 3.
To divide 2x^3 - 7x^2 + 2x + 3 by x - 3 using long division, follow these steps:
Step 1: Set up the long division as follows:
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x - 3 | 2x^3 - 7x^2 + 2x + 3
Step 2: Divide the first term of the dividend (2x^3) by the divisor (x - 3), which gives:
2x^2
Step 3: Multiply the previous quotient (2x^2) by the divisor (x - 3), and subtract the result from the dividend:
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x - 3 | 2x^3 - 7x^2 + 2x + 3
-(2x^3 - 6x^2)
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-x^2 + 2x + 3
Step 4: Bring down the next term from the dividend (-x^2):
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x - 3 | 2x^3 - 7x^2 + 2x + 3
-(2x^3 - 6x^2)
_____________________
-x^2 + 2x + 3
-( -x^2 + 3x)
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-x - 3
Step 5: Divide the next term (-x) by the divisor (x - 3):
-x / (x - 3) = -1
Step 6: Multiply the previous quotient (-1) by the divisor (x - 3), and subtract the result from the remaining expression:
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x - 3 | 2x^3 - 7x^2 + 2x + 3
-(2x^3 - 6x^2)
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-x^2 + 2x + 3
-( -x^2 + 3x)
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-x - 3
-( -x - 3)
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0
Step 7: Since the remaining expression is 0, the division is complete.
Result: The quotient is 2x^2 - x - 1, and the remainder is 0.