Which of the following is a factor of rs + tr - pt - ps?
(p - s)
(s - p)
(r - p)
(r + p)
Correct answer is C
rs + tr - pt - ps = rs - ps - tr - pt = (r - p)s + (r - p)t = (r - p)(s + t), hence r - p is a factor
(1 - a - b)(1 - a + b)
(1 + a - b)(1 - a + b)
(1 - a + b)(1 - a + b)
(1 + a + b)(1 + a + b)
Correct answer is B
1 - (a - b)2 = [1 + (a - b)][1 - a + b]
= (1 + a - b)(1 - a + b)
(m2 + 1)(m - 2)
(m - 1)(m + 1)(m + 2)
(m - 2)(m + 1)(m - 1)
(m2 + 2)(m - 1)
Correct answer is C
m3 - 2m2 - m + 2
Let f(m) = m3 - 2m2 - m2 + 2
= f(1)
= 1 - 2 - 2 + 2 = 0
∴ m - 1 is factor \(\frac{m^3 - 2m^2 - m^2 + 2}{m - 1}\)
= m2 - m - 2
= (m - 1)m2 - m - 2
= (m - 1)(m + 1)(m - 2)
If g(x) = x2 + 3x + 4, find g(x + 1) - g(x)
(x + 2)
2(x + 2)
(2x + 1)
(x2 + 4)
Correct answer is B
g(x) = x2 + 3x + 4
= g(x + 1) = (x + 1)^2 + 3(x + 1) + 4
= x2 + 1 + 2x + 3x + 3 + 4
= x2 + 5x + 8
g(x + 1) - g(x) = x2 + 5x + 8 - (x2 + 3x + 4)
= x2 + 5x + 8 - x2 + 3x + 4
= 2x + 4
= 2(x + 2)
uvw = 16(u + v)
16ur = 3w(u + v)
uvw = 12(u + v)
12uvw = u + v
Correct answer is C
W \(\alpha\) \(\frac{\frac{1}{uv}}{u + v}\)
∴ w = \(\frac{\frac{k}{uv}}{u + v}\)
= \(\frac{k(u + v)}{uv}\)
w = \(\frac{k(u + v)}{uv}\)
w = 8, u = 2 and v = 6
8 = \(\frac{k(2 + 6)}{2(6)}\)
= \(\frac{k(8)}{12}\)
k = 12
i.e 12 ( u + v) = uwv