Final answer:
To find the required polynomial for addition, set the expression equal to the desired sum and solve for the polynomial by subtracting one from the other, simplifying and combining like terms.
Step-by-step explanation:
To find the polynomial that, when added to 3x4 - 9x + 5x? - x + 7, will give a sum of 314x2 + 3x + 327, we can set up the equation as an addition problem. Since we are seeking a missing polynomial, let's call it 'P(x)' and set up the equation:
P(x) + (3x4 - 9x + 5x? - x + 7) = 314x2 + 3x + 327
Since 3x4 - 9x + 5x? - x + 7 contains unknowns and typos, we will ignore those parts per the student's instructions. Assuming '5x?' represents a typo, and it should be a term of the form 5xn where n is a positive integer. We can structure P(x) as:
P(x) = (314x2 + 3x + 327) - (3x4 - 9x - x + 7)
This gives us:
P(x) = 314x2 + 3x + 327 - 3x4 + 9x + x - 7
Now, combine like terms to get the polynomial:
P(x) = -3x4 + 314x2 + 13x + 320
This is the polynomial to be added to achieve the desired sum.