Question

divide 3x^4-5x^2+3 by x+2

Answer 1

Answer:

(3x^4-5x^2+3)=(3x^3-6,x^2+7x-14)(x+2)+31

Answer 2

Quotient   = 3x³ - 6x² + 7x  - 14 and remainder =  31 on dividing 3x⁴-5x²+3 by x + 2

Given:

• 3x⁴-5x²+3

To Find:

• Divide by x + 2

Solution:

• Dividend = Divisor x Quotient + remainder

Division algorithm :

• Stop the division if remainder is zero or degree of remainder is less than divisor
• f(x) = g(x)q(x) + r(x)
• r(x)= 0  or degree of r(x) less than degree of g(x)

Dividend = f(x) = 3x⁴-5x²+3

Divisor  = g(x) = x + 2

Using long division method

            3x³ - 6x² + 7x  - 14

           _____________

x + 2  )   3x⁴  -5x²  +  3   (

             3x⁴ + 6x³

          ________

                  -6x³ - 5x² + 3

                  -6x³ - 12x²        

                ____________

                          7x²  + 3

                          7x² + 14x

                         _______

                                -14x + 3

                                -14x - 28

                               _________

                                         31

Quotient q(x) = 3x³ - 6x² + 7x  - 14

remainder =  31