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Chapter 5: Problem 51

After dividing a polynomial by a binomial, explain how to check the answer.

Short Answer

Expert verified
To check the answer after dividing a polynomial by a binomial, utilize the relationship expressed by the equation A = B*Q + R. That is to say, multiply the divisor with the quotient, and then add in the remainder, if any. If the result equals the initial polynomial, the division process was correctly performed. Only then is the original division validated.

Step by step solution

01

Understand division of polynomials

Look at the division process. When a polynomial (let's say A) is divided by a binomial (let's say B), it gives us quotient (Q) and possibly a remainder (R). This division process can be expressed as: A = B*Q + R in which B is the divisor, Q is the quotient and R is the remainder.
02

Multiply divisor and quotient

To verify the correctness of the division, multiply the divisor B by the quotient Q. Write down the result after multiplication.
03

Add the remainder

Add the remainder R to the result of multiplication (B*Q). The sum should equal the original polynomial (A) if the division was done correctly.
04

Verify

To confirm that the division process was done correctly, compare the resultant expression with the initial polynomial. If they match, well done!

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