Math, asked by rima96, 8 months ago

when , divisor is (A2+2a-1), quotient is (5a-14),and Remainder is (35a-17).what is dividend ?​

Answers

Answered by isyllus
60

Given:

Divisor is a^2+2a-1

Quotient 5a-14

Remainder 35a-17

To find:

Dividend = ?

Solution:

The formula is:

Dividend = (Quotient \times Divisor) + Remainder

If we multiply the quotient and divisor and then add remainder to it, we will get the dividend.

First of all, let us multiply the quotient and divisor:

Quotient \times Divisor = (5a-14)

\Rightarrow 5a\times (a^2+2a-1)-14\times (a^2+2a-1)\\\Rightarrow 5a^3+10a^2-5a-14a^2-28a+14\\\Rightarrow 5a^3-4a^2-33a+14

Now adding remainder in the above term to find the dividend:

Quotient \times Divisor + Remainder:

\Rightarrow 5a^3-4a^2-33a+14 + 35a -17\\\Rightarrow 5a^3-4a^2+ 2a -3

So, the dividend is 5a^3-4a^2+ 2a -3.

Answered by mysticd
15

 Given , Divisor \: g(x)= (a^{2}+2a-1)

 Quotient\: q(x)  = 5a - 14

 Remainder \: r(x) = 35a - 17

 Let \: Dividend = p(x)

By Division Algorithm :

 \boxed{\pink{p(x) = g(x) \times q(x) + r(x) }}

 Dividend \:p(x)

 = g(x) \times q(x) + r(x)

 = (a^{2}+2a-1)(5a-14)+35a-17

 = a^{2}(5a-14)+2a(5a-14)-1(5a-14)+ 35a-17

 = 5 a^{3}-14a^{2}+10a^{2}-28a-5a+14+35a-17

 = 5a^{3} +(-14+10) a^{2} +(-28-5+35)a+14-17

 = 5a^{3} - 4a^{2}+2a-3

Therefore.,

 \red{Dividend } \green { = 5a^{3} - 4a^{2}+2a-3}

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