how do I solve this: (17x^3-5x^2+4x-3)-(5x^3-9x^2-8x+11) and putting the resulting polynomial in standard form?
just collect like powers of x:
17x^3-5x^2+4x-3
-(5x^3-9x^2-8x+11)
---------------------
12x^3 + 4x^2 + 12x - 14
To solve (17x^3 - 5x^2 + 4x - 3) - (5x^3 - 9x^2 - 8x + 11) and put the resulting polynomial in standard form, follow these steps:
1. Distribute the negative sign across the second polynomial:
(17x^3 - 5x^2 + 4x - 3) + (-5x^3 + 9x^2 + 8x - 11)
2. Group like terms together. Combine the x^3 terms, x^2 terms, x terms, and constant terms:
(17x^3 - 5x^3) + (-5x^2 + 9x^2) + (4x + 8x) + (-3 - 11)
Simplify:
12x^3 + 4x^2 + 12x - 14
3. Rearrange the terms in descending order of powers of x:
12x^3 + 4x^2 + 12x - 14
This is the resulting polynomial in standard form.