Question

What is the value of `p` such that `3x^p(4x^(2p+3) + 2x^(3p-2)) = 12x^12 + 6x^10`?

Answer 1

`p =3`

Explanation:

We have:

`3x^p(4x^(2p+3) + 2x^(3p-2)) = 12x^12 + 6x^10`

`:. 3x^p xx 4x^(2p+3) + 3x^p xx 2x^(3p-2) = 12x^12 + 6x^10`

`:. 12 x^(p+(2p+3)) + 6 x^(p+(3p-2)) = 12x^12 + 6x^10`

`:. 12 x^(3p+3) + 6 x^(4p-2) = 12x^12 + 6x^10`

Compare coefficients of `x^12` and `x^10` then:

`x^12: 3p+3 = 12 => p=3`
`x^10: 4p-2 = 10 => p=3`

And so with `p=3` both indices on the LHS are simultaneously identical to the RHS.