Factorize \(x^2 + 2a + ax + 2x\)
(x + 2a)(x + 1)
(x + 2a)(x - 1)
(x2 - 1)(x - a)
(x + 2)(x + a)
Correct answer is D
\(x^{2} + 2a + ax + 2x\)
\(x^{2} + 2a + ax + 2x\)
\(x(x + 2) + a(x + 2)\)
\((x + 2)(x + a)\)
x < 11
x < -1
x > 6
x > 11
Correct answer is D
\(\frac{1}{3}\)(x + 1) - 1 > \(\frac{1}{5}\)(x + 4)
= \(\frac{x + 1}{3}\) - 1 > \(\frac{x + 4}{5}\)
\(\frac{x + 1}{3}\) - \(\frac{x + 4}{5}\) - 1 > 0
= \(\frac{5x + 5 - 3x - 12}{15}\)
= 2x - 7 > 15
= 2x > 22
= x > 11
If y = \(\frac{x}{x - 3}\) + \(\frac{x}{x + 4}\) find y when x = -2
-\(\frac{3}{5}\)
\(\frac{3}{5}\)
-\(\frac{7}{5}\)
\(\frac{2}{5}\)
Correct answer is A
y = \(\frac{x}{x - 3}\) + \(\frac{x}{x + 4}\) when x = -2
y = \(\frac{-2}{-5}\) + \(\frac{(-2)}{-2 + 4}\)
= \(\frac{2}{5}\) + \(\frac{-2}{2}\)
= \(\frac{4 -10}{10}\)
= \(\frac{-6}{10}\)
= -\(\frac{3}{5}\)
Factorize completely 8a + 125ax3
(2a + 5x2)(4 + 26ax)
a(2 + 5x)(4 - 10x + 25x2)
(2a + 5x)(4 - 10ax + 25x2)
a(2 + 5x)(4 + 10ax + 25x2)
Correct answer is B
\(8a + 125ax^{3} = (2^{3})a + 5^{3} ax^{3}\)
= \(a(2^3 + 5^3 x^3)\)
∴\(a[2^3 + (5x)^3]\)
\(a^3 + b^3 = (a + b)(a^2 - ab + b^2)\)
∴ \(a(2^3 + (5x)^3)\)
= \(a(2 + 5x)(4 - 10x + 25x^2)\)
If x varies directly as y3 and x = 2 when y = 1, find x when y = 5
2
10
125
250
Correct answer is D
x \(\alpha\) y3
x = ky3
k = \(\frac {x}{y^3}\)
when x = 2, y = 1
k = 2
Thus x = 2y3 - equation of variation
= 2(5)3
= 250