Question

What must be added to 4x4+2x3-2x2+x-1 so that the resulting polynomial is divisible by x2-2x-3?
class 10 (polynomial )

Answer 1

91x + 89 is added to 4x⁴ + 2x³ - 2x² + x - 1 so that the resulting polynomial is divisible by x² - 2x - 3.

Given:

p(x) = 4x⁴ + 2x³ - 2x² + x - 1

g(x) = x² - 2x - 3

Step-by-step explanation:

x² - 2x - 3)4x⁴ + 2x³ - 2x² + x - 1(4x² + 10x + 30

                4x⁴ - 8x³ - 12x²          

                       10x³ + 10x² + x - 1

                      10x³ - 20x² - 30x  

                                 30x² + 31x - 1

                                30x² - 60x - 90

                                            91x + 89

∴ When the polynomial 91x + 89 is added to the polynomial 4x⁴ + 2x³ - 2x² + x - 1 then the added polynomial is completely divisible by x² - 2x - 3.

Answer 2

So,reminder = -61x+65

And, the quotient = 4x²-6x+22