Question

Divide $\left( 15{{y}^{4}}-16{{y}^{3}}+9{{y}^{2}}-\dfrac{1}{3}y-\dfrac{50}{9} \right)$ by $\left( 3y-2 \right)$
Given answer: $5{{y}^{3}}+2{{y}^{2}}-\dfrac{13}{3}y+\dfrac{25}{9}$.
A. True
B. False

Answer 1

Hint: In this question, we are given a question and its answer. We need to check if the answer is true or false. For this we will ourselves solve the sum. We will divide the polynomial by (3y-2) using a long division method. We will first learn all the steps involved and then solve our sum.

Complete step by step answer:
We are given the polynomial $\left( 15{{y}^{4}}-16{{y}^{3}}+9{{y}^{2}}-\dfrac{1}{3}y-\dfrac{50}{9} \right)$. We need to divide it by 3y-2. Let us use following steps:
(I) Let us make sure that the polynomial is written in descending order. Now let us divide the term with highest power inside the division symbol by the term with the highest power outside the division symbol.
(II) Let us multiply the answer obtained in the previous step by the polynomial in front of the division symbol.
(III) Let us subtract and bring down the next term.
(IV) Repeating steps 1, 2, 3 until there are no terms to bring down.

We have obtained the quotient as $5{{y}^{3}}-2{{y}^{2}}+\dfrac{5}{3}y+1$ and the remainder as $\dfrac{-32}{9}$.
But we are given the quotient (answer) as $5{{y}^{3}}+2{{y}^{2}}-\dfrac{13}{3}y+\dfrac{25}{9}$.
So the given answer is wrong.

So, the correct answer is “Option B”.

Note: Students can make mistakes with signs in these sums. They can get confused between quotient and remainder. If the answer is given then it means we are given a quotient. Before dividing, make sure that the dividend (polynomial which gets divided) is in descending order.