Question

Divide x^3+ 6x^2 - 11x+6 by x+5, write remainder. and quotient​

Answer 1

Answer:

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Answer 2

Answer:

Question :-

Divide x^3+ 6x^2 - 11x+6 by x+5, write remainder. and quotient

Required Answer :-

Quotient = x² + x - 16

Remainder = 86

Solution :-

$\bf \underline \red{Step \: 1 :-}$

To obtain the first term of the quotient, divide the highest degree term of dividend (i.e., x³) by the highest degree term of the divisor (i.e., x). This is x². Then carry out the division process. What remains is x² - 11x + 6.

$\bf \underline \red{Step \: 2 :-}$

Now, to obtain the second term of the quotient, divide the highest degree term of new dividend (i.e., x²) by the highest degree term of divisor (i.e., x). This gives x. Again carry out the division process with x² - 11x + 6.

$\bf \underline \red{Step \: 3 :-}$

We get -16x + 6, to obtain the third term of the quotient, divide the highest degree of new dividend (i.e.,-16x) by the highest degree term of divisor (i.e., x). This gives -16. then carry out the division process with -16x + 6.

$\bf \underline \red{Step \: 4 :-}$

What remains is 86. Now, the degree of 86 is less than the degree of the divisor x + 5. So, we cannot continue the division any further.

So, the quotient is x² + x - 16 and the remainder is 86.

Note :-

We stop the division process when either the remainder is zero or its degree is less than the degree of the divisor.