Question

1.What is the coefficient of the third term of the quotient when x5-2 by x+1?
A.-2
B.-1
C.1
D.2
2. What is the degree of the quotient when 2x7-2x³+2 is divided by x⁴-2x²-x+1?
A.2
B.3
C.4
D.5

Answer 1

Given  : x⁵ - 2  divided by x + 1

To Find : coefficient of the third term of the quotient

Solution:

              x⁴ - x³ + x² - x  + 1

x + 1   )   x⁵        - 2    (

             x⁵ + x⁴

             _____

              -x⁴          - 2

             -x⁴ - x³

            __________

                   x³          -2

                   x³ + x²

                 _________

                       -x²       -2

                       -x²  -x

                      _________

                               x  - 2

                               x  + 1

                              _____

                                   -3

remainder = -3

Quotient = x⁴ - x³ + x² - x  + 1

3rd term = x²

coefficient = 1

Correct option is  C) 1

2x⁷-2x³+2   is divided by x⁴-2x²-x+1

Degree of  Dividend  2x⁷-2x³+2  is 7

Degree of  Divisor x⁴-2x²-x+1  is 4

Degree of quotient = Degree of Dividend - Degree of Divisor

Degree of Quotient = 7 - 4  = 3

Hence correct option is B) 3

A polynomial is a monomial or a sum of monomials

Degree of a polynomial is the highest degree of its monomials.

When the exponents of all variables in a monomial are summed up, the resulting number is called the degree of the monomial.

A monomial is number, a variable, or a product of numbers and variables with whole number exponents.

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