Question

1 point Q.5 Write the quotient obtained on dividing (r? - b) a) by (x - b). (r+b)(x+a) b. (x-b)(x-a) (r+b)r-a d. (r +b)(x+a) a. C. O a. O b. O c. O d.​

Answer 1

Answer:

When we divide A by B in long division, Q is the quotient and R is the remainder. If we can write a number in this form then A mod B = R ...

Answer 2

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Write the quotient obtained on dividing (r? - b) a) by (x - b). (r+b)(x+a) b. (x-b)(x-a) (r+b)r-a d. (r +b)(x+a) a. C. O a. O b. O c. O d.

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The quotient remainder theorem

When we want to prove some properties about modular arithmetic we often make use of the quotient remainder theorem.

It is a simple idea that comes directly from long division.

The quotient remainder theorem says:

Given any integer A, and a positive integer B, there exist unique integers Q and R such that

A= B * Q + R where 0 ≤ R < B

We can see that this comes directly from long division. When we divide A by B in long division, Q is the quotient and R is the remainder.

If we can write a number in this form then A mod B = R

Examples

A = 7, B = 2

7 = 2 * 3 + 1

7 mod 2 = 1

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