Question

Use synthetic division to perform each division. x4-1 / x-1

Accepted Answer

Identify the divisor and the dividend. Here, the divisor is $$x - 1$$, and the dividend is $$x^4 - 1$. Set up synthetic division by writing the zero of the divisor x - 1 = 0$, which is x = 1$. Then list the coefficients of the dividend polynomial in descending order of degree. For x^4$ - 1$$, the coefficients are $$1 ($$for $$x^4$$), $$0 ($$for $$x^3$$), $$0 ($$for $$x^2$$), $$0 ($$for $$x$$), and $$-1 ($$constant term). Begin synthetic division by bringing down the first coefficient (which is 1) as is. Then multiply this number by the zero of the divisor (1), and write the result under the next coefficient. Add the column values and write the sum below. Repeat the multiply and add process for each coefficient until all coefficients have been processed. The numbers obtained at the bottom row (except the last one) represent the coefficients of the quotient polynomial. The last number is the remainder. Write the quotient polynomial using these coefficients with descending powers of $$x$$ starting from one degree less than the original polynomial.

Use synthetic division to perform each division. x⁴-1 / x-1

Verified video answer for a similar problem:

Key Concepts

Synthetic Division

Polynomial Coefficients

Remainder Theorem