Solving Polynomial Equations
Solve the following equation using factoring:
5x^2+5x=0
5x(x+1)=0; x=0,-1
Find where the rational expression is undefined, find the domain, and write the domain in interval notation.
1/(x+4)
Undefined at x=-4
Domain:
(-∞,-4)∪(-4,∞)
Simplify the expression:
(x^2+3x+2)+(2x^2-x+1)
3x^2+2x+3
Factor the following polynomial:
x^2-3x-10
(x-5)(x+2)
The length of a garden is 3 more than double the width. Write a simplified expression for the area of the garden.
Width: w Length: 2w+3
A=2w^2+3w
Solve the following equation using factoring:
x^3-4x=0
x(x+2)(x-2)=0; x=0,-2,2
Find where the rational expression is undefined, find the domain, and write the domain in interval notation.
(x+2)/(x^2-9)
Undefined at x= -3, 3
Domain:
(-oo,-3)∪(-3,3)∪(3, oo)
Simplify the expression:
(4x^2+2x+1)-(x^2-x+5)
3x^2+3x-4
Factor the following polynomial:
49x^2-64y^2
(7x+8y)(7x-8y)
A whiteboard has a width of x+2 and a length of x+5. Write a simplified expression for the area of the whiteboard.
Width: x+2 Length: x+5
A=x^2+7x+10
Solve the following equation using factoring:
2x^2+7x+3=0
(x+3)(2x+1)=0; x=-3,-1/2
Find where the rational expression is undefined, find the domain, and write the domain in interval notation.
(5x)/(x^2+x-6)
Undefined at x=-3, 2
Domain:
(-oo,-3)∪(-3,2)∪(2, oo)
Simplify the expression:
(9x^2+2x+1)-(4x^2-3x-5)
5x^2+5x+6
Factor the following polynomial:
20m^4n+30m^3n^2
10m^3n(2m+3n)
The length of a rectangular vegetable bed is x+3 and the width is 2x-4. Find a simplified expression for the area for the vegetable bed.
What are the dimensions if x=6?
Length:9 Width:8
2x^2+2x-12
Solve the following equation using grouping:
x^2-5x+3x-15
(x-5)(x+3)=0; x=-3,5
Find where the rational expression is undefined, find the domain, and write the domain in interval notation.
(4x-1)/(x^2-16x+63)
Undefined at: x=7, 9
Domain:
(-oo,7)∪(7,9)∪(9,oo)
Simplify the expression:
(x+2)(x^2+3x+4)
x^3+5x^2+10x+8
Factor the following polynomial using grouping:
x^2+2x+xy+2y
(x+2)(x+y)
A backyard patio has an area of x2-4x-21. What are the dimensions of the patio if x=9?
Dimensions: 2 x 12
Solve the following equation using factoring:
4x^2+4x-8=0
4(x+2)(x-1)=0; x=-2,1
Find where the rational expression is undefined, find the domain, and write the domain in interval notation.
(6x-9)/(x^2-x-6)
Undefined at: x=-2,3
Domain:
(-oo,-2)∪(-2,3)∪(3,oo)
Simplify the expression:
(x+5)(x^2-4x+6)
x^3+x^2-14x+30
Factor the following polynomial:
6x^2-x-12
(3x+4)(2x-3)
The area of a garden is 2x2+x-6. Find the dimensions of the garden if x=4.
Dimensions: 5 x 6