Question

F(x)=x³-6x²+11x-6 ; g(x) = x²+x+1 Find the quotient

Answer 1

Given : polynomial P(x) = x³ - 6x² + 11x - 6 is divided by polynomial g(x) = x² + x + 1.

To find : the quotient.

solution : let's find the quotient using long division method,

x² + x + 1 )x³ - 6x² + 11x - 6(x - 7

x³ + x² + x

............................................

-7x² + 10x - 6

-7x² - 7x - 7

...............................................

17x + 1

The quotient = (x - 7) and remainder = (17x + 1).

verification : using Euclid theorem, a = bq + r

LHS = p(x) = x³ - 6x² + 11x - 6

RHS = (x - 7) × g(x) + (17x + 1)

= (x - 7) × (x² + x + 1) + (17x + 1)

= x³ + x² + x - 7x² - 7x - 7 + 17x + 1

= x³ - 6x² + 11x - 6

LHS = RHS

Therefore the quotient is (x - 7).

also read similar questions : apply division algorithm to find quotient and remainder .

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Answer 2

Step-by-step explanation:

right answer

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