Write the polynomial as linear combinations of monic Legendre polynomials by using orthogonality to compute the coefficients.
$t^4+t^2$
My attempt:
Since I know that $q_4(t) = t^4-\frac{6t^2}{7}+\frac{3}{35}$ and $q_2(t)= t^2 -\frac{1}{3}$ then I must have a situation where the linear combinations looks like $\alpha q_4(t) +\beta q_2(t) +\gamma q_0(t)$where $\alpha , \beta, \gamma$ are constant coefficients. My question is how do I find those coefficients so that $\alpha q_4(t) +\beta q_2(t) +\gamma q_0(t)= t^4 +t^2$