The sixth number 20210A is prime for only one digit A. What is A?

9514 1404 393

  A = 9

Step-by-step explanation:

Beyond the first few primes, all prime numbers end in one of the odd digits, 1, 3, 7, or 9. We can reduce this list by using a couple of simple divisibility rules.

The sum of the digits is 2+0+2+1+0+A = A+5. The number will be divisible by 3 if A+5 is divisible by 3. That will be the case for A=1 and A=7.

The sum of odd digits is A+1+0 = A+1. The sum of even digits is 0+2+2 = 4. When these sums are equal, the number is divisible by 11. That will be the case for A=3.

So, we have ruled out all digits except 9. If the number is prime it must be ...

  202109

  A = 9

Additional comment

To make sure the number is prime, we would need to check divisibility by all primes less than √202109 ≈ 449.

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct

step-by-step explanation: