What is the quotient: (–3x3 + 16x2 + 13x – 6) ÷ (3x – 1) ?
Use polynomial long division.
You should get -5x^2 +5x +6
You are in luck. (3x-1) is an exact factor, with no remainder.
can you help me with this
Subtract 5x^2 + 2x -11 from 3x^2 + 8x -7 . Express the result as a trinomial.
To find the quotient of the given expression, we can use long division. Here's how you can do it:
Step 1: Divide the highest degree term of the dividend (–3x^3) by the highest degree term of the divisor (3x). The result is –x^2.
-x^2
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3x - 1 | -3x^3 + 16x^2 + 13x - 6
Step 2: Multiply the divisor (3x – 1) by the quotient obtained in step 1 (-x^2). Then, subtract the product from the dividend.
-x^2
x
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3x - 1 | -3x^3 + 16x^2 + 13x - 6
- (-3x^3 + x^2)
Simplify the expression after subtraction:
-x^2 + 16x^2 = 15x^2
x
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3x - 1 | -3x^3 + 16x^2 + 13x - 6
- (-3x^3 + x^2)
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15x^2 + 13x
Step 3: Repeat the process with the new expression. Divide the highest degree term of the simplified expression (15x^2) by the highest degree term of the divisor (3x). The result is 5x.
-x^2 + 5x
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3x - 1 | -3x^3 + 16x^2 + 13x - 6
- (-3x^3 + x^2)
________________
15x^2 + 13x
- (15x^2 - 5x)
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18x - 6
Step 4: Repeat the process with the new expression. Divide the highest degree term of the simplified expression (18x) by the highest degree term of the divisor (3x). The result is 6.
-x^2 + 5x + 6
________________
3x - 1 | -3x^3 + 16x^2 + 13x - 6
- (-3x^3 + x^2)
________________
15x^2 + 13x
- (15x^2 - 5x)
__________________
18x - 6
- (18x - 6)
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0
Step 5: Since there are no remaining terms to divide, the long division is complete. The quotient is -x^2 + 5x + 6.
Therefore, the quotient of (-3x^3 + 16x^2 + 13x – 6) ÷ (3x – 1) is -x^2 + 5x + 6.