The remainder when 6p3 - p2 - 47p + 30 is divided by p - 3 is
21
42
63
18
Correct answer is B
Let f(p) = 6p3 - p2 - 47p + 30
Then by the remainder theorem,
(p - 3): f(3) = remainder R,
i.e. f(3) = 6(3)3 - (3)2 - 47(3) + 30 = R
162 - 9 - 141 + 30 = R
192 - 150 = R
R = 42
If x - 4 is a factor of x2 - x - k, then k is
4
12
20
2
Correct answer is B
Let f(x) = x2 - x - k
Then by the factor theorem,
(x - 4): f(4) = (4)2 - (4) - k = 0
16 - 4 - k = 0
12 - k = 0
k = 12
If S = \(\sqrt{t^2 - 4t + 4}\), find t in terms of S
S2 - 2
S + 2
S - 2
S2 + 2
Correct answer is B
S = \(\sqrt{t^2 - 4t + 4}\)
S2 = t2 - 4t + 4
t2 - 4t + 4 - S2 = 0
Using \(t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
Substituting, we have;
Using \(t = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(4 - S^2)}}{2(1)}\)
\(t = \frac{4 \pm \sqrt{16 - 4(4 - S^2)}}{2}\)
\(t = \frac{4 \pm \sqrt{16 - 16 + 4S^2}}{2}\)
\(t = \frac{4 \pm \sqrt{4S^2}}{2}\)
\(t = \frac{2(2 \pm S)}{2}\)
Hence t = 2 + S or t = 2 - S
{3,5,7,11,17,19}
{3,5,11,13,17,19}
{3,5,7,11,13,17,19}
{2,3,5,7,11,13,17,19}
Correct answer is C
P = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}
Q = {-1, 3, 5, 7, 11, 13, 17, 19, 23}
P \(\cap\) Q = {3, 5, 7, 11, 13, 17, 19}
Simplify \(\frac{\sqrt{5}(\sqrt{147} - \sqrt{12}}{\sqrt{15}}\)
5
\(\frac{1}{5}\)
\(\frac{1}{9}\)
9
Correct answer is A
\(\frac{\sqrt{5}(\sqrt{147} - \sqrt{12}}{\sqrt{15}}\)
\(\frac{\sqrt{5}(\sqrt{49 \times 3} - \sqrt{4 \times 3}}{\sqrt{5 \times 3}}\)
\(\frac{\sqrt{5}(7\sqrt{3} - 2\sqrt{3}}{\sqrt{5} \times \sqrt{3}}\)
\(\frac{\sqrt{3} (7 - 2}{\sqrt{3}}\)
= 5