Simplify
Simplify the following
(x^3-3x^2-2x+5)-(x^2-2x+2)
x^3-4x^2+3
Write Prime Factorization of
1350
2*5^2*3^3
Factor Completely
4t^2+4t+1
(2t+1)(2t+1)
Solve the following
x^2-5x+6=0
(x+6)(x-1)=0
x=1,-6
Find the solution to the set
x^2+2x-8>0
(x+4)(x-2)>0
2,-4 are roots
x>2,x<-4
Simplify
(3t-4)(2t+3)
6t^2+t-12
Write the prime factorization of
91x^2y^3z
7*13*x^2*y^3*z
Factor Completely
3x^3-27x
3x(x^2-9)=3x(x+3)(x-3)
Find the zeros of the function
f(x)=x^3-4x
0=x^3-4x=x(x^2-4)=x(x+2)(x-2)
x=0,2,-2
A farmer plans to use 25m of fencing to enclose a rectangular pen that has an area of 63 m². Only three sides of the pen need fencing because part of an existing wall will be used for one of the longer sides. Find the dimensions of the pen.
l+2w=25
l=25-2w
l*w=63
w(25-2w)=63
-2w^2+25w-63=0
(-2w+7)(w-9)=0
w=9,7/2
l=7,18
Simplify
(-x^3)^2x^4
x^6*x^4=x^10
Find the Greatest Common Factor of
54s^2t^3, 90s^3t^2,108s^4t
54s^2t^3=2*3^3*s^2*t^3
90s^3t^2=2*3^2*5*s^3*t^2
108s^4t=2^2*3^3*s^4*t
GCF=2*3^2*s^2*t=18s^2t
Factor Completely
3x^2-4x-4
(3x+2)(x-2)
Solve for x
6x^2=5x-1
0=6x^2-5x+1=(3x-1)(2x-1)
x=1/2,1/3
A rocket is moving vertically upward with a speed of 245m/s when its fuel runs out. How much farther will it travel upward before it starts falling back to the ground?
h=vt-4.9t^2
0=245t-4.9t^2=2450t-49t^2
0=49t(50-t)
t=0,50sec
h=49(25)(50=25)
h=30625 m
Simplify
p(p-2q)+3(pq-q^2)
p^2-2pq+3pq-3q^2=p^2+pq-3q^2
Find the Least Common Multiple of
9a^2b^2c, 15a^2b^3,6a^3b^2
9a^2b^2c=3^2*a^2*b^2*c
15a^2b^3=3*5*a^2*b^3
6a^3b^2=2*3*a^3*b^2
LCM=2*3^2*a^3*b^3*c=18a^3b^3
Factor Completely
x^4-3x^2-4
(x^2+1)(x^2-4)=(x^2+1)(x-2)(x+2)
Solve. Identify any double roots if any
(u-2)^2-3u+8=0
0=(u^2-4u+4)-3u+8
0=u^2-7u+12=(u-3)(u-4)
u=3,4
Graph the solution to the set
x^3+x^2<2x
x^3+x^2-2x<0
x(x^2+x-2)<0
x(x+2)(x-1)<0
0,-2,1 are nodes
0<x<1 ,x<-2 graph with those
Simplify
xy^2(x+y)-x^2y(y-x)
x^2y^2+xy^3-x^2y^2+x^3y=xy^3+x^3y
Find the Greatest Common Factor and the Least Common Multiple of
12a^2b^2, 8ab^3, 16b^4
12a^2b^2=2^2*3*a^2*b^2
8ab^3=2^3*a*b^3
16b^4=2^4*b^4
GCF=2^2*b^2=4b^2
LCM=2^4*3*a^2*b^4=48a^2b^4
Factor Completely
x^2-x-a-a^2
(x^2-a^2)-(x+a)=(x-a)(x+a)-1(x+a)=(x-a-1)(x+a)
Solve. Identify any double roots if any.
(x-1)^3-(x-1)^2=0
(x-1)(x-1)^2-1(x-1)=0
0=(x-1-1)(x-1)^2=(x-2)(x-1)^2
x=2,1(double root)
When 0.5cm is planed off each of the six faces of a cube, its volume is decreased by 169cm cubed. Find its new volume
(x-1)^3=x^3-169
(x-1)(x^2-2x+1)=x^3-169
x^3-2x^2+x-x^2+2x-1=x^3-169
x^3-3x^2+3x-1=x^3-169
0=3x^2-3x-168
0=(3x-24)(x+7)=3(x-8)(x+7)
x=8cm
7^3=343cm^3