Vocabulary
Long/Box Division
Synthetic I
Synthetic II
Factor
100
The x^2+12
in (x^3-3x^2+12x-36)/(x^2+12)
The divisor
100
(x^3-9x^2-x+65)/(x-8)
x^2-x-9-7/(x-8)
100
(n^5-15n^4+44n^3+20n^2+54n-20)/(n-5)
n^4-10n^3-6n^2-10n+4
100
(10x^4+x^3-20x-4)/(10x+1)
x^3-2+(-2)/(10x+1)
100
The quotient of (x^2-2x-15)/(x-5) is (x+3) . Write it in factored form.
(x+3)(x-5)=x^2-2x-15
200
(Polynomial) Long Division
200
(x^3-5x^2+2x+1)/(x-4)
x^2-x-2-7/(x-4)
200
(a^4+a^3-66a^2+44a-90)/(a+9)
a^3-8a^2+6a-10
200
(4p^5-17p^4-4p^3+2p^2+36p)/(4p-1)
p^4-4p^3-2p^2+9+9/(4p-1)
200
The quotient of (p^3+16p^2+59p-6)/(p+6) is p^2+10p-1 . Write it in factored form.
(p+6)(p^2+10p-1)=p^3+16p^2+59p-6
300
In the dividend of (x^3-3x^2+12x-36)/(x^2+12)
this is the number 3 or "3rd"
the highest degree
300
(32x^4-12x^3-43x^2+27x-4)/(8x^2+7x-4)
4x^2-5x+1
300
(9n^5-36n^4+81n^3-99n^2-45n+87)/(9n-9)
n^4-3n^3+6n^2-5n-10+(-1)/(3n-3)
300
Factor x^3+4x^2+3x+12=0
(x+4)(x^2+3)=0
400
(Polynomial) Synthetic Division
400
(6x^4-27x^3+13x^2+43x-14)/(3x^2-3x-7)
2x^2-7x+2
400
(a^5+a^4+a-9)/(a+1)
a^4+1+(-10)/(a+1)
400
(8a^4-23a^3-12a^2+67a+54)/(8a+9)
a^3-4a^2+3a+5+9/(8a+9)
400
Factor x^4-x^3+x^2-x=0
x(x-1)(x^2+1)=0
500
What is the "16" called in this picture
the remainder
500
Find the original dividend from this quotient:
k^3-10k^2-5k+4-2/(2k+5)
2k^4-15k^3-60k^2-17k+18
500
(4p^5-17p^4-4p^3+2p^2+36p)/(p-1/4)
4p^4-16p^3-8p^2+36+9/(p-1/4)
500
(5p^5+p^4-14p^3-22p^2+49p-28)/(5p-4)
p^4+p^3-2p^2-6p+5+(-8)/(5p-4)
500
Factor x^3+2x^2-x-2=0
(x+2)(x-1)(x+1)=0