Multiplying Polynomials
6v(2v+3)
12v2+18v
p2 + m; use m = 1, and p = 5
26
8r3− 64r2 + r − 8
(8r2 + 1)(r − 8)
Factor. (k + 1)(k − 5) = 0
{−1, 5}
Working alone, Ryan can dig a 10 ft by 10 ft hole in five hours. Castel can dig the same hole in six hours. How long would it take them if they worked together?
2.73 hours
−4(v + 1)
−4v − 4
x + y + y; use x = 9, and y = 10
29
6v3− 16v2+ 21v − 56
(2v2 + 7)(3v − 8)
Factor. (a + 1)(a + 2) = 0
{−1, −2}
Working together, Paul and Daniel can pick forty bushels of apples in 4.95 hours. Had he done it alone it would have taken Daniel 9 hours. Find how long it would take Paul to do it alone.
11 hours
(2n + 2)(6n + 1)
12n2 + 14n + 2
6q + m − m; use m = 8, and q = 3
18
63n3+ 54n2− 105n − 90
3(3n2 − 5)(7n + 6)
Factor. x2 − 11x + 19 = −5
{3, 8}
Working alone, it takes Kristin 11 hours to harvest a field. Kayla can harvest the same field in 16 hours. Find how long it would take them if they worked together.
6.52 hours
(8p − 2)(6p + 2)
48p2 + 4p − 4
(y + x) ÷ 2 + x; use x = 1, and y = 1
2
28v3 + 16v2 − 21v − 12
(4v2 − 3)(7v + 4)
Factor. n2 + 7n + 15 = 5
{−5, −2}
Ryan can paint a fence in ten hours. Sanji can paint the same fence in eight hours. If they worked together how long would it take them?
4.44 hours
(5n + 6)(5n − 5)
25n2 + 5n − 30
z − (y ÷ 3 − 1); use y = 3, and z = 7
7
24r3 − 64r2 − 21r + 56
(8r2 − 7)(3r − 8)
Factor. n2+ 3n − 12 = 6
{3, −6}
Krystal can wax a floor in 16 minutes. One day her friend Perry helped her and it only took 5.76 minutes. How long would it take Perry to do it alone?
9 minutes