If (x+2) and (3x−1) are factors of 6x3+x2−19x+6, find the third factor.
2x−3
3x+1
x−2
3x+2
Correct answer is A
To get the third factor, take the product of the other 2 factors and then divide the main equation by their product.
64.245
61.255
60.255
60.245
Correct answer is C
(1.98)6=(1+0.98)6=1+6(0.98)+15(0.98)2+20(0.98)3+15(0.98)4+6(0.98)5+(0.98)6
≊
= 60.255
Simplify \frac{1 + \sqrt{8}}{3 - \sqrt{2}}
7 + \sqrt{2}
7 + 7\sqrt{2}
1 - 7\sqrt{2}
1 + \sqrt{2}
Correct answer is D
\frac{1 + \sqrt{8}}{3 - \sqrt{2}}
Rationalizing by multiplying through with 3 + \sqrt{2},
(\frac{1 + \sqrt{8}}{3 - \sqrt{2}})(\frac{3 + \sqrt{2}}{3 + \sqrt{2}}) = \frac{3 + \sqrt{2} + 3\sqrt{8} + 4}{9 - 2}
= \frac{3 + \sqrt{2} + 3\sqrt{4 \times 2} + 4}{7}
= \frac{7 + 7\sqrt{2}}{7} = 1 + \sqrt{2}
If 8^{x} ÷ (\frac{1}{4})^{y} = 1 and \log_{2}(x - 2y) = 1, find the value of (x - y)
\frac{5}{4}
\frac{3}{5}
1
\frac{2}{3}
Correct answer is A
8^{x} ÷ (\frac{1}{4})^{y} = 1
(2^{3})^{x} ÷ (2^{-2})^{y} = 2^{0}
2^{3x - (-2y)} = 2^{0}
\implies 3x + 2y = 0 .... (1)
\log_{2}(x - 2y) = 1
x - 2y = 2^{1} = 2 ..... (2)
Solving equations 1 and 2,
x = \frac{1}{2}, y = \frac{-3}{4}
(x - y) = \frac{1}{2} - \frac{-3}{4} = \frac{5}{4}
If f(x) = 3x^{3} + 8x^{2} + 6x + k and f(2) = 1, find the value of k.
-67
-61
61
67
Correct answer is A
f(x) = 3x^{3} + 8x^{2} + 6x + k
f(2) = 3(2^{3}) + 8(2^{2}) + 6(2) + k = 1
\implies 24 + 32 + 12 + k = 1
68 + k = 1 \therefore k = 1 - 68 = -67