1. (9x^4 + 7x^2 - 6x - 15) **+** (3x^3 - 7x^2 + 6x - 15) = **
9x^4 + 3x^3 - 30**

(9x^4+7x^2-6x-15) **-** (3x^3-7x^2+6x-15) = **9x^4 - 3x^3 +14x^2 - 12x**

2. I hope I am interpreting this correctly

(9m^{4}n^{2 }- 13m^{3}n^{3 }+ 11m^{2}n^{4})
**+**(-4m^{2}-n^{4}-3m^{4}n^{2}-m^{3}n^{3}) =
**6m**^{4}n^{2} - 14m^{3}n^{3} + 7m^{2}n^{4 }- n^{4}

(9m^{4}n^{2} - 13m^{3}n^{3} + 11m^{2}n^{4}) - (-4m^{2 }- n^{4 }- 3m^{4}n^{2 }- m^{3}n^{3})=
**12m**^{4}n^{2 }-12m^{3}n^{3} + 15m^{2}n^{4} + n^{4}

3. and 4. Ibadan, now that you've seen how to work a couple of these, why not try the next two on your own. If you run into any difficulty, send me a message and I'll help you.

5. (2x^{3} - 4x^{2} -7x +19) + ? = (x^{2} + 3x +24)

You can treat the question mark just as if it were some other variable.

Therefore

? = (x^{2} + 3x +24) - (2x^{3} - 4x^{2} -7x +19)

? = -2x^{3} +5x^{2} +10x +5