Which of the following is the correct factorization of the polynomial below? 27^3+64

19747 = 7^2×13×31

Step-by-step explanation:

Factor the following integer:

19747

Since sqrt(19747)≈140.5, it is sufficient to test 19747 for divisibility by primes less than or equal to 140.:

Test primes up to 140 for factors of 19747.

19747 is not divisible by 2 since 19747 is odd and 2 is even:

19747 = 19747 (19747 is not divisible by 2)

The sum of the digits of 19747 is 1 + 9 + 7 + 4 + 7 = 28, which is not divisible by 3. This means 19747 is not divisible by 3:

19747 = 19747 (19747 is not divisible by 2 or 3)

The last digit of 19747 is not 5 or 0, which means 19747 is not divisible by 5:

19747 = 19747 (19747 is not divisible by 2, 3 or 5)

Divide 7 into 19747:

| | 2 | 8 | 2 | 1 | (quotient)

7 | 1 | 9 | 7 | 4 | 7 |  

- | 1 | 4 | | | |  

| | 5 | 7 | | |  

| - | 5 | 6 | | |  

| | | 1 | 4 | |  

| | - | 1 | 4 | |  

| | | | 0 | 7 |  

| | | | - | 7 |  

| | | | | 0 | (remainder)

19747 = 7×2821 (2821 is not divisible by 2, 3 or 5 since 19747 is not)

Divide 7 into 2821:

| | 4 | 0 | 3 | (quotient)

7 | 2 | 8 | 2 | 1 |  

- | 2 | 8 | | |  

| | 0 | 2 | |  

| | - | 0 | |  

| | | 2 | 1 |  

| | - | 2 | 1 |  

| | | | 0 | (remainder)

19747 = 7×7×403 (403 is not divisible by 2, 3 or 5 since 2821 is not)

Divide 7 into 403:

| | 5 | 7 | (quotient)

7 | 4 | 0 | 3 |  

- | 3 | 5 | |  

| | 5 | 3 |  

| - | 4 | 9 |  

| | | 4 | (remainder)

403 is not divisible by 7:

19747 = 7×7×403 (403 is not divisible by 2, 3, 5 or 7)

The alternating sum of the digits of 403 is 4 - 0 + 3 = 7, which is not divisible by 11. This means 403 is not divisible by 11:

19747 = 7×7×403 (403 is not divisible by 2, 3, 5, 7 or 11)

Divide 13 into 403:

| | | 3 | 1 | (quotient)

1 | 3 | 4 | 0 | 3 |  

| - | 3 | 9 | |  

| | | 1 | 3 |  

| | - | 1 | 3 |  

| | | | 0 | (remainder)

19747 = 7×7×13×31 (31 is not divisible by 2, 3, 5, 7 or 11 since 403 is not)

31 is not divisible by any prime less than sqrt(31)≈5.5 (namely 2, 3 or 5). Therefore 31 is prime:

19747 = 7×7×13×31

There are 2 copies of 7, 1 copy of 13 and 1 copy of 31 in the product:

 19747 = 7^2×13×31

$97520

step-by-step explanation:

add 6% to the value she got from selling the house.

c.

step-by-step explanation:

because first you have to add the 4x, 9x, and the 7x together and you get 20x and then you add the last numbers up and you get 5and then you put the subtraction sign in there and that's how you get the answer.