Divide 2x\(^{3}\) + 11x\(^2\) + 17x + 6 by 2x + 1.
x2 + 5x + 6
2x2 + 5x - 6
2x2 + 5x + 6
x2 - 5x + 6
Correct answer is A
No explanation has been provided for this answer.
Make \(\frac{a}{x}\) the subject of formula \(\frac{x + 1}{x - a}\) = m
\(\frac{m - 1}{m + 1}\)
\(\frac{m + 1}{1 - m}\)
\(\frac{m - 1}{1 + m}\)
\(\frac{m + 1}{m - 1}\)
Correct answer is A
\(\frac{x + a}{x - a}\) = m
x + a = mx - ma
a + ma = mx - x
a(m + 1) = x(m - 1)
\(\frac{a}{x}\) = \(\frac{m - 1}{m + 1}\)
Solve for the equation \(\sqrt{x}\) - \(\sqrt{(x - 2)}\) - 1 = 0
\(\frac{3}{2}\)
\(\frac{2}{3}\)
\(\frac{4}{9}\)
\(\frac{9}{4}\)
Correct answer is D
\(\sqrt{x}\) - \(\sqrt{(x - 2)}\) - 1 = 0
= \(\sqrt{x}\) - \(\sqrt{(x - 2)}\) = 1
= (\(\sqrt{x}\) - \(\sqrt{(x - 2)}\))2 = 1
= x - 2 \(\sqrt{x(x - 2)}\) + x -2 = 1
= (2x - 3)2 = [2 \(\sqrt{x(x - 4)}\)]2
= 4x2 - 12x + 9
= 4(x2 - 2x)
= 4x2 - 12x + 9
= 4x2 - 8x
4x = 9
x = \(\frac{9}{4}\)
Factorize r2 - r(2p + q) + 2pq
(r - 2q)(2r - p)
(r - p)(r + p0
(r - q)(r - 2p)
(2r - q)(r + p)
Correct answer is C
r2 - r(2p + q) + 2pq = r2 - 2pr -qr + 2pq
= r(r - 2p) - q(r - 2p)
= (r - q)(r - 2p)
2, -1
-1, 2
3, -2
-2, 3
Correct answer is B
pm2 + qm + 1 = (m - 1) Q(x) + 2
p(1)2 + q(1) + 1 = 2
p + q + 1 = 2
p + q = 1.....(i)
pm2 + qm + 1 = (m - 1)Q(x) + 4
p(-1)2 + q(-1) + 1 = 4
p - q + 1 = 4
p - q = 3....(ii)
p + q = 1, p - q = -3
2p = -2, p = -1
-1 + q = 1
q = 2