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Concept explainers
To calculate: The quotient and remainder when the polynomial
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Answer to Problem 15AYU
The quotient is
Explanation of Solution
Given information:
The polynomial
Formula used:
When a polynomial is divided by its factor then dividend is the product of divisor and quotient increased by remainder.
Calculation:
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 five 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
Now, when a polynomial is divided by its divisor then dividend is the product of divisor and quotient increased by remainder.
To verify multiply the terms on the right hand side,
Thus, the quotient is
Chapter A Solutions
Precalculus
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