Question
If $p(m)=m^3+2 m^2-m+10$, then $P(a)+p(-a)=$ ?
✓
Answer
$p(m)=m^3+2 m^2-m+10$
Put $m = a$ in the given polynomial.
$\therefore p(a)=a^3+2 a^2-a+10$
Put $m=-a$ in the given polynomial.
$p(-a)=(-a)^3+2(-a)^2-(-a)+10$
$\therefore p(-a)=-a^3+2 a^2+a+10 \ldots$
Adding (i) and (ii),
$p(a)+p(-a)=\left(a^3+2 a^2-a+10\right)+\left(-a^3+2 a^2+a+10\right)$
$=a^3-a^3+2 a^2+2 a^2-a+a+10+10$
$\therefore p(a)+p(-a)=4 a^2+20$
Put $m = a$ in the given polynomial.
$\therefore p(a)=a^3+2 a^2-a+10$
Put $m=-a$ in the given polynomial.
$p(-a)=(-a)^3+2(-a)^2-(-a)+10$
$\therefore p(-a)=-a^3+2 a^2+a+10 \ldots$
Adding (i) and (ii),
$p(a)+p(-a)=\left(a^3+2 a^2-a+10\right)+\left(-a^3+2 a^2+a+10\right)$
$=a^3-a^3+2 a^2+2 a^2-a+a+10+10$
$\therefore p(a)+p(-a)=4 a^2+20$
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