Question

What is the quotient (2x3 − 3x2 − 14x + 15) ÷ (x − 3)?

Answer 1

2x^2 + 3x - 5

Hope this helps!

Answer 2

Answer:  The correct option is (a) $2x^2+3x-5.$

Step-by-step explanation:  We are given to find the quotient in the following division :

$Q=\dfrac{2x^3-3x^2-14x+15}{x-3}.$

To find the quotient, first we will try to factorize the numerator and then we will try to divide by the denominator.

We have

$Q\\\\\\=\dfrac{2x^3-3x^2-14x+15}{x-3}\\\\\\=\dfrac{2x(x-3)+3x(x-3)-5(x-3)}{x-3}\\\\\\=\dfrac{(x-3)(2x^2+3x-5)}{(x-3)}\\\\=2x^2+3x-5.$

Thus, the required coefficient is $2x^2+3x-5.$

Option (a) is CORRECT.