If p(m) = m3 + 2m2 – m + 10, then P(a) + p(-a) = ?

1.	If p(m) = m3 + 2m2 – m + 10, then P(a) + p(-a) = ?
Answer» p(m) = m³ + 2m² – m + 10 Put m = a in the given polynomial. ∴ p(a) = a³ + 2a² – a + 10 …(i) Put m = -a in the given polynomial. p(-a) = (-a)³ + 2(-a)² – (-a) +10 ∴ p (-a) = -a³ + 2a² + a + 10 …(ii) Adding (i) and (ii), p(a) + p(-a) = (a³ + 2a² – a + 10) + (-a³ + 2a² + a + 10) = a³ – a³ + 2a² + 2a² – a + a + 10 + 10 ∴ p(a) + p(-a) = 4a² + 20

Answer»

p(m) = m³ + 2m² – m + 10

Put m = a in the given polynomial.

∴ p(a) = a³ + 2a² – a + 10 …(i)

Put m = -a in the given polynomial.

p(-a) = (-a)³ + 2(-a)² – (-a) +10

∴ p (-a) = -a³ + 2a² + a + 10 …(ii)

Adding (i) and (ii),

p(a) + p(-a) = (a³ + 2a² – a + 10) + (-a³ + 2a² + a + 10)

= a³ – a³ + 2a² + 2a² – a + a + 10 + 10

∴ p(a) + p(-a) = 4a² + 20

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