다항식 전체 문제

Divide Polynomials using Synthetic Division

In the following exercises, use synthetic Division to find the quotient and remainder.

${x}^{4}+{x}^{2}+6x-10$ is divided by $x+2$

Divide Polynomials using Synthetic Division

In the following exercises, use synthetic Division to find the quotient and remainder.

$2{x}^{4}-9{x}^{3}+5{x}^{2}-3x-6$ is divided by $x-4$

Divide Polynomial Functions

In the following exercises, divide.

For functions $f(x)={x}^{2}-13x+36$ and $g(x)=x-4,$ find ⓐ $\left(\frac{f}{g}\right)(x)$ ⓑ $\left(\frac{f}{g}\right)(-1)$

Divide Polynomial Functions

In the following exercises, divide.

For functions $f(x)={x}^{2}-15x+54$ and $g(x)=x-9,$ find ⓐ $\left(\frac{f}{g}\right)(x)$ ⓑ $\left(\frac{f}{g}\right)(-5)$

Divide Polynomial Functions

In the following exercises, divide.

For functions $f(x)={x}^{3}+{x}^{2}-7x+2$ and $g(x)=x-2,$ find ⓐ $\left(\frac{f}{g}\right)(x)$ ⓑ $\left(\frac{f}{g}\right)(2)$

Divide Polynomial Functions

In the following exercises, divide.

For functions $f(x)={x}^{3}+2{x}^{2}-19x+12$ and $g(x)=x-3,$ find ⓐ $\left(\frac{f}{g}\right)(x)$ ⓑ $\left(\frac{f}{g}\right)(0)$

Divide Polynomial Functions

In the following exercises, divide.

For functions $f(x)={x}^{2}-3x+2$ and $g(x)=x+3,$ find ⓐ $\left(\frac{f}{g}\right)(x)$ ⓑ $\left(\frac{f}{g}\right)(3)$

Divide Polynomial Functions

In the following exercises, divide.

For functions $f(x)={x}^{2}+2x-3$ and $g(x)=x+3$ find ⓐ $\left(\frac{f}{g}\right)(x)$ⓑ $\left(\frac{f}{g}\right)(3)$

Use the Remainder and Factor Theorem

In the following exercises, use the Remainder Theorem to find the remainder.

$f(x)={x}^{3}-8x+7$ is divided by $x+3$

Use the Remainder and Factor Theorem

In the following exercises, use the Remainder Theorem to find the remainder.

$f(x)={x}^{3}-4x-9$ is divided by $x+2$

Use the Remainder and Factor Theorem

In the following exercises, use the Remainder Theorem to find the remainder.

$f(x)=2{x}^{3}-6x-24$ divided by $x-3$

Use the Remainder and Factor Theorem

In the following exercises, use the Remainder Theorem to find the remainder.

$f(x)=7{x}^{2}-5x-8$ divided by $x-1$

In the following exercises, use the Factor Theorem to determine if $x-c$ is a factor of the polynomial function.

Determine whether $x+3$ a factor of ${x}^{3}+8{x}^{2}+21x+18$

In the following exercises, use the Factor Theorem to determine if $x-c$ is a factor of the polynomial function.

Determine whether $x+4$ a factor of ${x}^{3}+{x}^{2}-14x+8$

In the following exercises, use the Factor Theorem to determine if $x-c$ is a factor of the polynomial function.

Determine whether $x-2$ a factor of ${x}^{3}-7{x}^{2}+7x-6$

In the following exercises, use the Factor Theorem to determine if $x-c$ is a factor of the polynomial function.

Determine whether $x-3$ a factor of ${x}^{3}-7{x}^{2}+11x+3$

James divides $48y+6$ by 6 this way: $\frac{48y+6}{6}=48y.$ What is wrong with his reasoning?

Divide $\frac{10{x}^{2}+x-12}{2x}$ and explain with words how you get each term of the quotient.

Explain when you can use synthetic division.

Types of Polynomials

In the following exercises, determine the type of polynomial.

$16{x}^{2}-40x-25$