Factoring Polynomials
Factor the polynomial:
x3+7x2+10x
x(x+5)(x+2)
Use Synthetic Division to divide the following equation:
(x2-3x-40)/ (x+5)
x-8
Divide the polynomial by long division.
(3x2+7x-20) / (x+4)
3x-5
What is the polynomial identity for a sum of cubes? (you can use any two variables-but recall I used a & b in the equation during the lesson)
a3+b3=(a2-ab+b2)
Factor the polynomial: (you will get a complex number solution)
8x3=1
1/2, (-1 +/- i sqrt3)/4
Factor the polynomial:
9x3+6x2-3x
3x(3x-1)(x+1)
Use Synthetic Division to solve the following equation:
(x3+3x2-x+2)/(x-1)
x2+4x+3, R:5
Use Long Division to solve the following equation:
2x3-3x2-18x-8) / (x-4)
2x2+5x+2
What is the general equation for a difference of squares? (Remember, I used a & b in the equation during the lesson)
a2-b2=(a+b)(a-b)
Factor the polynomial: (you will get a complex number solution)
x4-12x2=64
x=+/-4,+/-2i
Factor the polynomial and find the zeros:
3x3+12x2-3x=12
x=-4,-1,1
Use Synthetic Division to solve the following equation:
(x3+27) / (x+3)
x2-3x+9
Use Long Division to solve the following equation:
(x2-7x+10)/ (x+3)
x-10, R:40
The following is an example of which identity?
8x3-1=(2x-1)(4x2+2x+1)
Difference of cubes
Factor the polynomial: (you will get a complex number solution)
x4+4x2=12
+/- sqrt2, +/- i sqrt 6
Factor the polynomial to find the zeros. You may need to use the quadratic equation.
12x3=60x2+75x
x=0, (5 +/- 5sqrt2) /2
Use Synthetic Division to solve the following equation:
(x4+3x3+x+4) / (x+3)
x3-3x2+12x-35, R:109
Use Long Division to solve the following equation:
(x3+5x2-3x-1) / (x-1)
x2+6x+3, R:2
The following is an example of which identity?
x2+10x+25=(x+5)2
Perfect Square Trinomials
Factor the polynomial: (you will get a complex number solution)
81x3-192=0
x= 4/3, (-2 +/- 2i sqrt 3)/3
Factor the polynomial to find the zeros.
x3+1=x2+x
x=-1,1
Use Synthetic Division to solve the following equation:
(x5+1) / (x+1)
x4-x3+x2-x+1
Use Long Division to solve the following equation:
(2x2+x-7) / (x-5)
2x+11, R:48
The following is an example of which identity?
x3-125
Difference of cubes
Factor the polynomial: (you will get a complex number solution)
x3+x2+x+1=0
x=-1,+/-i