3.5 Dividing polynomials  (Page 4/6)

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?

$\left(x^2+5x-1\right)÷\left(x-1\right)$

$\left(2x^2-9x-5\right)÷\left(x-5\right)$

$\left(3x^2+23x+14\right)÷\left(x+7\right)$

$\left(4x^2-10x+6\right)÷\left(4x+2\right)$

$\left(6x^2-25x-25\right)÷\left(6x+5\right)$

$\left(-x^2-1\right)÷\left(x+1\right)$

$\left(2x^2-3x+2\right)÷\left(x+2\right)$

$\left(x^3-126\right)÷\left(x-5\right)$

$\left(3x^2-5x+4\right)÷\left(3x+1\right)$

$\left(x^3-3x^2+5x-6\right)÷\left(x-2\right)$

$\left(2x^3+3x^2-4x+15\right)÷\left(x+3\right)$

$\left(3x^3-2x^2+x-4\right)÷\left(x+3\right)$

$\left(2x^3-6x^2-7x+6\right)÷(x-4)$

$\left(6x^3-10x^2-7x-15\right)÷(x+1)$

$\left(4x^3-12x^2-5x-1\right)÷(2x+1)$

$\left(9x^3-9x^2+18x+5\right)÷(3x-1)$

$\left(3x^3-2x^2+x-4\right)÷\left(x+3\right)$

$\left(-6x^3+x^2-4\right)÷\left(2x-3\right)$

$\left(2x^3+7x^2-13x-3\right)÷\left(2x-3\right)$

$\left(3x^3-5x^2+2x+3\right)÷(x+2)$

$\left(4x^3-5x^2+13\right)÷(x+4)$

$\left(x^3-3x+2\right)÷\left(x+2\right)$

$\left(x^3-21x^2+147x-343\right)÷\left(x-7\right)$

$\left(x^3-15x^2+75x-125\right)÷\left(x-5\right)$

$\left(9x^3-x+2\right)÷\left(3x-1\right)$

$\left(6x^3-x^2+5x+2\right)÷\left(3x+1\right)$

$\left(x^4+x^3-3x^2-2x+1\right)÷\left(x+1\right)$

$\left(x^4-3x^2+1\right)÷\left(x-1\right)$

$\left(x^4+2x^3-3x^2+2x+6\right)÷\left(x+3\right)$

$\left(x^4-10x^3+37x^2-60x+36\right)÷\left(x-2\right)$

$\left(x^4-8x^3+24x^2-32x+16\right)÷\left(x-2\right)$

$\left(x^4+5x^3-3x^2-13x+10\right)÷\left(x+5\right)$

$\left(x^4-12x^3+54x^2-108x+81\right)÷\left(x-3\right)$

$\left(4x^4-2x^3-4x+2\right)÷\left(2x-1\right)$

$\left(4x^4+2x^3-4x^2+2x+2\right)÷\left(2x+1\right)$

$x-2,4x^3-3x^2-8x+4$

$x-2,3x^4-6x^3-5x+10$

$x+3,-4x^3+5x^2+8$

$x-2,4x^4-15x^2-4$

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

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

Factor is $x^2-x+3$

Factor is $(x^2+2x+4)$

Factor is $x^2+2x+5$

Factor is $x^2+x+1$

Factor is $x^2+2x+2$

$\frac{4x^3-33}{x-2}$

$\frac{2x^3+25}{x+3}$

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

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

$\frac{x^4-22}{x+2}$

Consider $\frac{x^k-1}{x-1}$ with $k=1, 2, 3.$ What do you expect the result to be if $k=4?$

Consider $\frac{x^k+1}{x+1}$ for $k=1, 3, 5.$ What do you expect the result to be if $k=7?$

Consider $\frac{x^4-k^4}{x-k}$ for $k=1, 2, 3.$ What do you expect the result to be if $k=4?$

Consider $\frac{x^k}{x+1}$ with $k=1, 2, 3.$ What do you expect the result to be if $k=4?$

Consider $\frac{x^k}{x-1}$ with $k=1, 2, 3.$ What do you expect the result to be if $k=4?$

$\frac{x+1}{x-i}$

$\frac{x^2+1}{x-i}$

$\frac{x+1}{x+i}$

$\frac{x^2+1}{x+i}$

$\frac{x^3+1}{x-i}$

Length is $x+5,$ area is $2x^2+9x-5.$

Length is $2x+5,$ area is $4x^3+10x^2+6x+15$

Length is $3x–4,$ area is $6x^4-8x^3+9x^2-9x-4$

Volume is $12x^3+20x^2-21x-36,$ length is $2x+3,$ width is $3x-4.$

Volume is $18x^3-21x^2-40x+48,$ length is $3x–4,$ width is $3x–4.$

Volume is $10x^3+27x^2+2x-24,$ length is $5x–4,$ width is $2x+3.$

Volume is $10x^3+30x^2-8x-24,$ length is $2,$ width is $x+3.$

Volume is $\pi (25x^3-65x^2-29x-3),$ radius is $5x+1.$

Volume is $\pi (4x^3+12x^2-15x-50),$ radius is $2x+5.$

Volume is $\pi (3x^4+24x^3+46x^2-16x-32),$ radius is $x+4.$