Please help me!

Setting the polynomial = 0 and factoring, we have

(a -7)(a-3) = 0  ..... so a = 7 or a = 3

And for all a > 7, the polynomial is postive.

So, the greatest "a" that makes the polynomial ≤ 0 is when a = 7.

If you change the problem to this:  a² - 10a + 21  =  0

Then, factoring:                            (a - 7)(a - 3)  =  0    --->  a = 3 or a = 7.

Going back to your original problem, an inequalty:  ≤ 0:

If you try any number (in the original problem) smaller than 3, your answer is positive; they don't work.

If you try any number from 3 through 7, your answer is negative; they all work, with the largest number = 7.

If you try any number larger than 7, your answer is positive; they don't work.