Question

Check whether x²+3x+1 is a factor of 3x⁴+5x³-7x²+2x+2

Answer 1

for answer plz rever to the image

Answer 2

Answer:

(x²+3x+1) is a factor of (3x⁴+5x³-7x²+2x+2)

Step-by-step explanation:

we have to Check whether (x²+3x+1) is a factor of  (3x⁴+5x³-7x²+2x+2)

let us perform a simple, normal division to find if it is a factor:

divisor = (x²+3x+1)

dividend = (3x⁴+5x³-7x²+2x+2)

if we get remainder '0' , then (x²+3x+1) is a factor of  (3x⁴+5x³-7x²+2x+2)

x²+3x+1 ) 3x⁴+5x³-7x²+2x+2 ( 3x² - 4x + 2

               3x⁴+9x³+3x²

               -------------------------

               0  - 4x³ - 10x² + 2x + 2

                   - 4x³ - 12x² - 4x

                  ----------------------------------

                      0 + 2x² + 6x + 2

                          + 2x² + 6x + 2

                          ----------------------

                                 0

here the remainder is '0'.

so , (x²+3x+1) is a factor of  (3x⁴+5x³-7x²+2x+2)