Question

Use synthetic division to divide the given polynomials:

a) Quotient
b) Remainder
c) Divisor
d) Coefficient

Answer 1

To use synthetic division, follow the steps: write in descending order, divide highest degree term, multiply and subtract, repeat until done.

Step-by-step explanation:

To use synthetic division, follow these steps:

1. Write the numerator and divisor in descending order of exponents and align like terms.
2. Divide the coefficient of the highest degree term in the numerator by the coefficient of the highest degree term in the divisor.
3. Multiply the result from step 2 by each term in the divisor and write the products below the corresponding terms in the numerator.
4. Add the terms in the numerator to the terms from step 3.
5. Repeat steps 2-4 until you have subtracted all terms in the divisor.

The quotient is the terms in the numerator after the final step, and the remainder is the constant term (if any) left after division. The divisor is the polynomial being divided, and the coefficient refers to the numerical factor in front of the variable term.