Question

10x^3+5x^2+75x-40 ÷2x+1​

Answer 1

Step-by-step explanation:

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Answer 2

Concept:

If the divisor is ' d ' and Dividend is ' D ' and quotient is ' q ' and remainder is ' r ', then we can express in mathematical word,

D = d * q + r

Given:

Given the divisor = 2x + 1 and the dividend is = $10x^3+5x^+75x-40$ for long polynomial division.

Find:

We have to find the quotient and remainder found by above long polynomial division.

Solution:

Given the division is,

Divisor = 2x + 1

Dividend = $10x^3+5x^+75x-40$

Doing the polynomial long division we get,

So, the quotient $=5x^2+\frac{75}{2}$

and the remainder = - 155/2

Now we can say that,

$10x^3+5x^+75x-40=(2x+1)(5x^2+\frac{75}{2})+(-\frac{155}{2})$

Hence the quotient of polynomial long division is $=\mathbf{5x^2+\frac{75}{2}}$ and the remainder is = - 155/2.

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