Question

Using the long division method, determine the remainder when the polynomial
4x^5 + 2x^4 - x^3 + 4x^2 - 7 is divided by (x - 1)
PLEASE ANSWER FAST !!!!

Answer 1

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Answer 2

Given:

The given polynomial is P(x) = 4x⁵ + 2x⁴ - x³ + 4x² - 7

Divisor is f(x) = (x - 1)

Find:

The remainder by the long division method.

Answer:

The remainder is 2.

Solution:

Long division method

Dividend = P(x) = 4x⁵ + 2x⁴ - x³ + 4x² - 7

Divisor = f(x) = (x - 1)

(x - 1) $\overline{)4x^5+2x^4-x^3+4x^2-7(}$ 4x⁴ + 6x³ + 5x² + 9x + 9

         4x⁵ - 4x⁴

       -       +      

                  6x⁴ - x³

                  6x⁴ - 6x³

                -        +    

                          5x³ + 4x²

                          5x³ - 5x²

                        -        +      

                                   9x²  - 7

                                   9x² - 9x

                                  -       +    

                                            9x - 7

                                            9x - 9

                                          -      +  

                                                 2  

∴ Quotient = 4x⁴ + 6x³ + 5x² + 9x + 9

Remainder = 2

Hence, the remainder is 2.

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