Basics and Operations
Identify the third-degree binomial: 2y-xy3+7 or 3x2y+5xy?
3x2y+5xy (The other is 4th degree)
Multiply: -7y2(-2y4+y2-1)
14y6-7y4+7y2
Factor out the GCF: 6x3-12x2+18x
6x(x2-2x+3)
Find the Prime Factorization of 140.
2 * 2 * 5 * 7
Write in Standard Form: 3x3-5x+7x4-9-x2
7x4+3x3-x2-5x-9
Multiply: (3x-2)(3x+2)
9x2-4
Factor: x2-3x-10
(x-5)(x+2)
A square picture has a 2-in frame. The frame area is 72 sq in. What is the picture area?
49 sq in (9 * 9 picture, 13 * 13 total with frame)
Which pair of factors of -60 has a sum of 7?
12 and -5
Multiply: (2y-6)2
4y2-24y+36
Factor: 36y2-1
(6y-1)(6y+1)
Find the area expression for a portrait where height is 1.5w and there is a 4-in frame.
(w+8)(1.5w+8)
Simplify: (3x3+7x-1) + (4x3-9x2-11x+1)
7x3-9x2-4x
(4x2+6)(x2-3x+8)
4x4-12x3+38x2-18x+48
Factor completely: 12y2-6y-90
6(y-3)(2y+5)
A cone has volume V=3pi y2+30pi y+75pi and height h=9. Find radius r.
r = y+5
Simplify: (-5x+7) - (x2-3x+2)
-x2-2x+5
Find the product: (2x - 3)(x2 + 4x - 5)
2x3 + 5x2 - 22x + 15
Factor completely: 20x2 - 10x - 100
10(2x - 5)(x + 2)
A rectangle width w has height 2w. Find the area with a 3-in frame.
2w2 + 18w + 36