To explain: The better method among long division and synthetic division when a polynomial is divided by
Answer to Problem 28AYU
The better method to divide the polynomials when divided by
Explanation of Solution
Given information:
The two methods to divided a polynomial by
To divide a polynomial by linear polynomial whose leading coefficient is 1 and is of the form
Synthetic division is the compact form of long division and is much simpler in terms of notation.
The value of c does not change the decision of choosing the better method of dividing the polynomials.
For example: consider the provided polynomial
To divide the polynomial
Here dividend is
Step 1: List down the coefficients of dividend in the descending powers of x, that are
Now, the divisor is of the form
Step 2: To perform the synthetic division put the coefficients in the division sign along with
Step 3: Bring down
Step 4: Multiply
Step 5: Now, add the elements of column 2 of row 1 and row 2.
Step 6: Multiply
Step 7: Now, add the elements of column 3 of row 1 and row 2.
Step 8: Multiply
Step 9: Now, add the elements of column 4 of row 1 and row 2.
Repeat the above steps 8 and 9 for remaining elements of first row,
Now, the first four elements of row 3 are coefficients of quotient in descending powers of x with degree one less than dividend and the last entry is remainder.
Therefore, quotient is
Thus, the better method to divide the polynomials when divided by
Chapter A Solutions
Precalculus
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