나머지정리와 인수정리

For the following exercises, find the dimensions of the right circular cylinder described.

The radius is $\frac{1}{3}$ meter greater than the height. The volume is $\frac{98}{9}\pi$ cubic meters.

For the following exercises, use long division to find the quotient and remainder.

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

For the following exercises, use long division to find the quotient and remainder.

$\frac{3{x}^{4}-4{x}^{2}+4x+8}{x+1}$

For the following exercises, use synthetic division to find the quotient. If the divisor is a factor, then write the factored form.

$\frac{{x}^{3}-2{x}^{2}+5x-1}{x+3}$

For the following exercises, use synthetic division to find the quotient. If the divisor is a factor, then write the factored form.

$\frac{{x}^{3}+4x+10}{x-3}$

For the following exercises, use synthetic division to find the quotient. If the divisor is a factor, then write the factored form.

$\frac{2{x}^{3}+6{x}^{2}-11x-12}{x+4}$

For the following exercises, use synthetic division to find the quotient. If the divisor is a factor, then write the factored form.

$\frac{3{x}^{4}+3{x}^{3}+2x+2}{x+1}$

For the following exercises, use the Rational Zero Theorem to help you solve the polynomial equation.

$2{x}^{3}-3{x}^{2}-18x-8=0$

For the following exercises, use the Rational Zero Theorem to help you solve the polynomial equation.

$3{x}^{3}+11{x}^{2}+8x-4=0$

For the following exercises, use the Rational Zero Theorem to help you solve the polynomial equation.

$2{x}^{4}-17{x}^{3}+46{x}^{2}-43x+12=0$

For the following exercises, use the Rational Zero Theorem to help you solve the polynomial equation.

$4{x}^{4}+8{x}^{3}+19{x}^{2}+32x+12=0$

For the following exercises, use Descartes’ Rule of Signs to find the possible number of positive and negative solutions.

${x}^{3}-3{x}^{2}-2x+4=0$

For the following exercises, use Descartes’ Rule of Signs to find the possible number of positive and negative solutions.

$2{x}^{4}-{x}^{3}+4{x}^{2}-5x+1=0$

If division of a polynomial by a binomial results in a remainder of zero, what can be conclude?

If a polynomial of degree $n$ is divided by a binomial of degree 1, what is the degree of the quotient?

For the following exercises, use long division to divide. Specify the quotient and the remainder.

$({x}^{2}+5x-1)\div (x-1)$

For the following exercises, use long division to divide. Specify the quotient and the remainder.

$(2{x}^{2}-9x-5)\div (x-5)$

For the following exercises, use long division to divide. Specify the quotient and the remainder.

$(3{x}^{2}+23x+14)\div (x+7)$

For the following exercises, use long division to divide. Specify the quotient and the remainder.

$(4{x}^{2}-10x+6)\div (4x+2)$

For the following exercises, use long division to divide. Specify the quotient and the remainder.

$(6{x}^{2}-25x-25)\div (6x+5)$