Precalculus Examples

Find the Factors Using the Factor Theorem
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Divide using synthetic division and check if the remainder is equal to . If the remainder is equal to , it means that is a factor for . If the remainder is not equal to , it means that is not a factor for .
Place the numbers representing the divisor and the dividend into a division-like configuration.
The first number in the dividend is put into the first position of the result area (below the horizontal line).
Multiply the newest entry in the result by the divisor and place the result of under the next term in the dividend .
Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.
All numbers except the last become the coefficients of the quotient polynomial. The last value in the result line is the remainder.
The remainder from dividing is , which means that is a factor for .
is a factor for
Find all the possible roots for .
If a polynomial function has integer coefficients, then every rational zero will have the form where is a factor of the constant and is a factor of the leading coefficient.
Divide by .
Division by Zero
Division by Zero
The final factor is the only factor left over from the synthetic division.
The factored polynomial is .

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