Factoring trinomials
Factor completely: x2+8x+12
(x+6)(x+2)
Factor completely: 2x2+7x+3
(2x+1)(x+3)
Factor completely:
4x2-9
(2x+3)(2x-3)
Factor completely: 14n2+10n
2n(7n+5)
The shorter side of a rectangle is 3 less than the longer side. The area is 54. Find the length and width.
9 units by 6 units
Factor completely:
m2-11m+18
(m-9)(m-2)
Factor completely: 5n2+26n+5
(5n+1)(n+5)
Factor completely: 81x2-1
(9x+1)(9x-1)
Factor completely: 18x3-6x
6x(3x2-1)
When 10 is subtracted from the square of a number the result is three times the number. What is the positive solution?
5
Factor completely: x2+5x-24
(x+8)(x-3)
Factor completely:
3x2-10x+7
(3x-7)(x-1)
Factor completely: 4x2-16
(2x+4)(2x-4)
Factor completely:
20m2+5m-15
5(4m-3)(m+1)
The difference of the squares of two consecutive even integers is 68. What are these numbers?
16,18
Factor completely:
y2-6y-7
(y-7)(y+1)
Factor completely:
7x2-36x+5
(7x-1)(x-5)
Factor completely: 25x2+30x+9
(5x+3)(5x+3)
Factor completely:
mx2-18mx+81m
m(x-9)2
Find three consecutive positve odd integers such that the product of the first and third is one more than four times the second.
3, 5, 7
Factor completely: x2-x-56
(x-8)(x+7)
Factor completely:
2x2-12x+10
2(x-1)(x-5)
Factor completely:
9x2-16y2
(3x+4y)(3x-4y)
Factor completely:
26y-6y2-8
2(y-4)(-3y+1)
A rectangular garden is surrounded by a walk of uniform width. The area of the garden is 180 square yards. If the dimensions of the garden plus the walk are 16 yards by 24 yards, find the dimensions of the garden.
18 ft by 10 ft