Explain how to answer. x 4 + 2 x 2 − 2 x − 3 x 2 + 7 x + 10 Divide x 4 + 2 x 2 − 2 x − 3 x 2 + 7 x + 10 using polynomial long division. Please show step by step as I am unsure.

Question

Explain how to answer.                     x                  4                    +      2              x                  2                    −      2      x      −      3                      x                  2                    +      7      x      +      10      Divide                    x                  4                    +      2              x                  2                    −      2      x      −      3                      x                  2                    +      7      x      +      10      using polynomial long division. Please show step by step as I am unsure.

Kendall Ponce · Accepted Answer

x    4    +  2      x    2    −  2  x  −  3  =  =      x    4    +  7      x    3    +  10      x    2    −  7      x    3    −  49      x    2    −  70  x  +  41      x    2    +  287  x  +  410  −  219  x  −  413  =  =  (      x    2    −  7  x  +  41  )  (      x    2    +  7  x  +  10  )  −  219  x  −  413  ,which says                    x        4            +      2              x        2            −      2      x      −      3                      x        2            +      7      x      +      10        =      x    2    −  7  x  +  41  +            −      219      x      −      413                      x        2            +      7      x      +      10        .Also we can use        x    2    +  7  x  +  10  =  (  x  +  2  )  (  x  +  5  )and the Polynomial remainder theorem, but it&#039;s very ugly.

Kendra Hudson · Accepted Answer

Hint:  (      x    4    +  2      x    2    −  2  x  −  3  )  −  (      x    2    )  (      x    2    +  7  x  +  10  )  =  −  7      x    3    −  8      x    2    −  2  x  −  3  (  −  7      x    3    −  8      x    2    −  2  x  −  3  )  −  (  −  7  x  )  (      x    2    +  7  x  +  10  )  =  ⋯

Explain how to answer. (x^4 + 2x^2-2x-3)/(x^2+ 7x+10) using polynomial long division. Please show step by step as I am unsure.

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