How can the division algorithm be used to check the result of polynomial division?

Deacon House
2022-09-11
Answered

How can the division algorithm be used to check the result of polynomial division?

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Isaiah Haynes

Answered 2022-09-12
Author has **16** answers

The division algorithm can be shown as f(x)=d(x)*q(x)+r(x), where in f(x) is the dividend, d(x) is the divisior, q(x) is the quotient and r(x) is the remainder. This division algorithm is used to check the result of polynomial division by solving the equation, in which the result should be equal.

Result:

Solving the equation of the division algorithm that it should be equal.

Result:

Solving the equation of the division algorithm that it should be equal.

asked 2021-01-19

Perform the indicated divisions.

$\frac{{x}^{2}-7x-78}{x+6}$

asked 2022-09-10

Use the Remainder Theorem to find the remainder for each division. State whether the binomial is a factor of the polynomial. $$(4{x}^{3}-7x+1)\xf7(x+\frac{1}{2})$$

asked 2022-09-22

You can use polynomial division to find that

$$\frac{{x}^{3}-7x+6}{x-2}={x}^{2}+2x-3$$

Is this equation true for all values of x? Explain.

$$\frac{{x}^{3}-7x+6}{x-2}={x}^{2}+2x-3$$

Is this equation true for all values of x? Explain.

asked 2022-09-10

Use synthetic division to perform the division.

$$\frac{{x}^{4}-9{x}^{3}+{x}^{2}-7x-20}{x-9}$$

$$\frac{{x}^{4}-9{x}^{3}+{x}^{2}-7x-20}{x-9}$$

asked 2022-05-07

Compute $$(-903)\xf7(-21)$$.

asked 2022-05-09

What is negative five hundred ninety divided by negative ten?

asked 2022-09-23

If you are using the Factor Theorem and synthetic division to find real zeros of a given polynomial, how can Descartes' Rule of Signs increase the efficiency of the process?