Answer:
(x + 3)(x² – 3x + 7)
Step-by-step explanation:
To express x³ + 2x + 21 in the form of (x + 3)(px² + qx + r),
we need to divide (x³ + 2x + 21) by
(x + 3), since (x + 3) is a factor of
(x³ + 2x + 21)
See attached photo on how to divide (x³ + 2x + 21) by (x + 3).
From the attached photo,
(x³ + 2x + 21)/ (x + 3) = x² – 3x + 7
Therefore,
x³ + 2x + 21 => (x + 3)(px² + qx + r)
x³ + 2x + 21 => (x + 3)(x² – 3x + 7)
