The factors of y 3 − 27 are ______________. A) (y−3) and ( y 2 + 3 y + 9 ); B) (y−3) and ( y 2 − 3 y − 9 ); C) (y+3) and ( y 2 + 3 y + 9 ); D) (y+3) and ( y 2 − 3 y − 9 )

Question

The factors of       y    3    −  27 are ______________. A) (y−3) and   (      y    2    +  3  y  +  9  ); B) (y−3) and   (      y    2    −  3  y  −  9  );  C) (y+3) and   (      y    2    +  3  y  +  9  );  D) (y+3) and   (      y    2    −  3  y  −  9  )

Royce Mathis · Accepted Answer

The correct answer is  A     (  y  −  3  ) and   (      y    2    +  3  y  +  9  )We have       y    3    −  27  =      y    3    −      3    3  We know that        a    3    −      b    3    =  (  a  −  b  )  (      a    2    +  a  b  +      b    2    )Here, the query is formatted as follows        a    3    −      b    3  , where a =  y and b = 3.  ∴      y    3    −      3    3    =  (  y  −  3  )  (      y    2    +  3  y  +      3    2    )    =  (  y  −  3  )  (      y    2    +  3  y  +  9  )

The factors of y^3−27 are ______________. A) (y−3) and (y^2+3y+9); B) (y−3) and (y^2−3y−9); C) (y+3) and (y^2+3y+9); D) (y+3) and (y^2−3y−9)

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