Question

What is the quotient when −3x3 + 5x + 14 is divided by x − 2?
−3x2 − 6x − 7
− 3x2 − x + 12
−3x2 + 6x − 7 + 28 over the quantity of x minus 2
−3x2 − x + 12 + 28 over the quantity of x minus 2

Answer 1

The answer is A. -3x2 - 6x - 7

Answer 2

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 :

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