Divide −3x^3−4x^2+ 4x +3 by x−3
A. -3x^2 + 2x + 24
B. -3x^2 -10x -16, R(-29)
C. -3x^2 -10x-16
D. -3x^2+2x+24, R 35
B. -3x^2 -10x -16, R(-29)
Not only did the bot get the wrong answer, but each of the choices
is incorrect
(−3x^3−4x^2+ 4x +3) ÷ (x-3)
= -3x^2 - 13x - 35 with remainder of -102
To divide −3x^3−4x^2+ 4x +3 by x−3, we can use long division.
First, set up the long division:
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x - 3 | -3x^3 - 4x^2 + 4x + 3
Now, let's perform the division step by step:
-3x^2 will be the first term of the quotient. Multiply by x - 3 to get -3x^3 + 9x^2.
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x - 3 | -3x^3 - 4x^2 + 4x + 3
-3x^3 + 9x^2
Subtract -3x^3 + 9x^2 from -3x^3 - 4x^2 to get -13x^2. Bring down the next term.
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x - 3 | -3x^3 - 4x^2 + 4x + 3
-3x^3 + 9x^2
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-13x^2
Now, divide -13x^2 by x - 3. The result is -13x.
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x - 3 | -3x^3 - 4x^2 + 4x + 3
-3x^3 + 9x^2
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-13x^2
+13x^2
Subtract -13x^2 + 13x^2 to get 0. Bring down the next term.
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x - 3 | -3x^3 - 4x^2 + 4x + 3
-3x^3 + 9x^2
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-13x^2
+13x^2
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4x
Now, divide 4x by x - 3. The result is 4.
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x - 3 | -3x^3 - 4x^2 + 4x + 3
-3x^3 + 9x^2
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-13x^2
+13x^2
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4x
+ 4x
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0
We have reached a remainder of 0, indicating that the division is complete.
Therefore, the quotient is -3x^2 + 2x + 4.
The correct answer is C. -3x^2 - 10x - 16.
To divide the polynomial −3x^3−4x^2+ 4x +3 by x−3, you can use long division. Here's step-by-step guidance on how to do it:
1. Start by determining the highest power of x in the dividend (−3x^3−4x^2+ 4x +3). In this case, it's x^3. Divide this term by the highest power of x in the divisor (x−3), which is x. The result is −3x^2.
-3x^2
2. Multiply the entire divisor (x−3) by the quotient you just found (-3x^2). The result is −3x^3 + 9x^2.
-3x^2 + ...
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x−3 | -3x^3−4x^2+ 4x +3
-3x^3+ 9x^2
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3. Subtract the result (−3x^3 + 9x^2) from the dividend (−3x^3−4x^2+ 4x +3). This will eliminate the x^3 term.
-3x^2 + ...
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x−3 | -3x^3−4x^2+ 4x+3
-(-3x^3+ 9x^2)
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-13x^2+ 4x
4. Bring down the next term from the dividend, which is 4x. Now, you have a new dividend, which is -13x^2+ 4x.
-3x^2 + ...
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x−3 | -3x^3−4x^2+ 4x+3
-(-3x^3+ 9x^2)
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-13x^2+ 4x
-13x^2+39x
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-35x + 3
5. Repeat step 1 to step 4 with the new dividend (-13x^2+ 4x) until there are no more terms left to bring down.
-3x^2 + 2x + 24
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x−3 | -3x^3−4x^2+ 4x+3
-(-3x^3+ 9x^2)
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-13x^2+ 4x
-(-13x^2+39x)
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-35x + 3
-(-35x + 105)
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102
6. So, the division result is -3x^2 + 2x + 24, and the remainder is 102.
Therefore, the correct answer is option D: -3x^2+2x+24, R 102.