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algol13
3 years ago
5

What is the quotient when −3x3 + 5x + 14 is divided by x − 2?

Mathematics
2 answers:
ASHA 777 [7]3 years ago
6 0
The answer is A. -3x2 - 6x - 7
Anika [276]3 years ago
6 0

Answer:

-3x^{2} -6x-7

Step-by-step explanation:

The given expression is :

\frac{-3x^{3}+5x+14}{x-2}

Factoring -3x^{3}+5x+14

Factor out common term -1

3x^{3}-5x-14

Now dividing leading coefficients of numerator and divisor.

\frac{3x^{3}}{x}=3x^{2}

Multiplying x-2 with 3x^{2} = 3x^{3}-6x^{2}

Subtracting 3x^{3}-6x^{2} from 3x^{3}-5x-14

we get 6x^{2} -5x-4

Therefore, \frac{-3x^{3}+5x+14}{x-2} = 3x^{2} +\frac{6x^{2}-5x-14}{x-2}

Now repeating these same steps until (x-2) is factored out, we get the quotient as :

-3x^{2} -6x-7

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