# Add the following polynomials: (3x^2 - 5x - 7) and (-9x^3 + 4x^2 - 9)

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The sum of the polynomials (3x^2 - 5x - 7) and (-9x^3 + 4x^2 - 9) has to be determined.

3x^2 - 5x - 7 + (-9x^3) + 4x^2 - 9

take the terms with the same power of x together

=> -9x^3 + 3x^2 + 4x^2 - 5x - 7 - 9

=> -9x^3 + 7x^2 - 5x - 16

**The sum of (3x^2 - 5x - 7) and (-9x^3 + 4x^2 - 9) is -9x^3 + 7x^2 - 5x - 16**

In the summation of polynomial, the coefficient of the term with the same variable should be added together.

For example, x^2 with the coefficient 3 should be added to 4x^2, resulting in (4+3)x^2 = 7x^2

In this way, the calculation can be done:

(3x^2-5x-7)+(-9x^3+4x^2-9) = -9x^3+(3+4)x^2-5x-(7+9)

= -9x^3+7x^2-5x-16