Question

How to use synthetic division to factor a function?

A) Divide the function by a linear factor to find the quotient.
B) Multiply the function by a linear factor to find the product.
C) Use long division to factor the function.
D) Multiply the function by a quadratic factor to find the product.

Answer 1

To use synthetic division to factor a function, divide the function by a linear factor to find the quotient. This helps determine if the linear factor is a root or zero of the function.

Step-by-step explanation:

To use synthetic division to factor a function, you divide the function by a linear factor to find the quotient. This process helps you determine if the linear factor is a root or zero of the function. Here are the steps to use synthetic division:

1. Write the function in the form f(x) = ax^n + bx^(n-1) + ... + k, where a, b, ..., k are coefficients.
2. Choose the linear factor in the form (x - r), where r is a possible root or zero of the function.
3. Set up the synthetic division table, placing the coefficient values of the function in reverse order in the top row and the chosen linear factor in the second row.
4. Perform the synthetic division by dividing each coefficient in the top row by the chosen linear factor's coefficient until you reach the constant term.
5. The resulting quotient in the synthetic division table represents the factored form of the function, with the linear factor as one of the factors.