Question

if 81x^5+27x^3-9x^2+50 is divided by (3x+2) then remainder is A, then find the value of 3a-42/10

Answer 1

3a-42/10
= 3*82/3-42/10
=82-42/10
=820-42/10
=778/10
=389/5


Hope it helps you

Answer 2

Given,

Polynomial $81x^5+27x^3-9x^2+50$, when divided by $3x+2$, remainder = A.

To find,

3A - 42/10

Solution,

Firstly, according to the remainder theorem, when a polynomial p(x) is divided by (x - a), the remainder obtained will be p(a).

It means if we substitute the value of x obtained by equating the divisor to 0 into the p(x), we get the remainder.

So here, the divisor is (3x + 2).

Putting 3x + 2 = 0, we get

$x = -\frac{2}{3}$

Let the given polynomial be: p(x).

Now, we can substitute the obtained value of x into p(x) to get the remainder.

As $p(x) =81x^5+27x^3-9x^2+50$

⇒ $p(-\frac{2}{3})=81(-\frac{2}{3})^5+27(-\frac{2}{3})^3-9(-\frac{2}{3})^2+50$

⇒ $p(-\frac{2}{3})=81(-\frac{32}{243})+27(-\frac{8}{27})-9(\frac{4}{9})+50$

⇒ $p(-\frac{2}{3})=(-\frac{32}{3})-8-4+50$

⇒ $p(-\frac{2}{3})=-\frac{32}{3}+38$

⇒ $p(-\frac{2}{3})=\frac{-32+114}{3}$

⇒ $p(-\frac{2}{3})=\frac{82}{3}$

Thus, the remainder when given p(x) is divided by 3x + 2, will be $\frac{82}{3} .$

Now, according to the question, the remainder is A. So,

$A=\frac{82}{3}$

We have to find

$3A-\frac{42}{10}$

Substituting the value of A,

$3A-\frac{42}{10}=3(\frac{82}{3} )-\frac{42}{10}$

$=82-\frac{42}{10}$

$=\frac{820-42}{10}$

$=\frac{778}{10}$

$=\frac{389}{5}$

Therefore, for the given polynomial, the value of $3A-\frac{42}{10}$ will be $\frac{389}{5}.$