Question

Find the value of a, if x + 2 is a factor of 4x⁴ + 2x³ − 3x² + 8x + 5a.

Answer 1

\[\text{We have to find the value of a if} (x + 2) \text{is a factor of} (4 x^4 + 2 x^3 - 3 x^2 + 8x + 5a) . \]
\[\text{Substituting}\ x = - 2\ \text{in}\ 4 x^4 + 2 x^3 - 3 x^2 + 8x + 5a, \text{we get:} \]
\[4( - 2 )^4 + 2( - 2 )^3 - 3( - 2 )^2 + 8( - 2) + 5a = 0\]
\[or, 64 - 16 - 12 - 16 + 5a = 0\]
\[or, 5a = - 20\]
\[or, a = - 4\]
\[ \therefore If (x + 2) \text{is a factor of}\ (4 x^4 + 2 x^3 - 3 x^2 + 8x + 5a), a = - 4 . \]