Factorize 4a2 - 12ab - C2 + 9b2
4a(a - 3b) + (3b - c)2
(2a + 3b - c)(2a + 3b + c)
(2a - 3b + c)(2a - 3b - c)
4a(a - 3b) + (3b + c)
Correct answer is C
4a2 - 12ab - C2 + 9b2
rearranges: (4a2 - 12ab + 9b2) - c2
(2a - 3b)(2a - 3b) - c2 = (2a - 3b)2 - c2
= (2a - 3b + c)(2a - 3b - c)
Factorize completely \(y^3 -4xy + xy^3 - 4y\)
(y + xy)(y + 2)(y - 2)
(y - xy)(y - 2)
y(1 + x)(y + 2)(y -2)
y(1 - x)(y + 2)(y - 2)
Correct answer is C
\(y^3 -4xy + xy^3 - 4y \)
= \(y^3(1 + x) - 4y(1 + x)
\((y^3 - 4y)(1 + x) = (y^3(1 + x) - 4y(1 + x))\)
∴ = \(y(1 + x)(y + 2)(y - 2)\)
Simplify \(\frac{324 - 4x^2}{2x + 18}\)
2(x - 9)
2(9 + x)
81 - x2
-2(x - 9)
Correct answer is D
\(\frac{324 - 4x^2}{2x + 18}\) = \(\frac{18^2 - (2x)^2}{2x + 18}\)
= \(\frac{(18 - 2x)(18 + 2x)}{(2x + 18)}\)
18 - 2x = 2(9 - x)
or -2(x - 9)
Solve for a positive number x such that \(2^{(x^3 - x^2 - 2x)} = 1\)
4
3
2
1
Correct answer is C
\(2^{(x^3 - x^2 - 2x)} = 1\)
\(x^3 - x^2 - 2x = 0\)
\(x(x^2 - x - 2) = 0\)
\(x^2 - x - 2 = 0\)
\((x + 1)(x - 2) = 0\)
x = 2 is the positive answer.
If \(f(x) = 2x^2 - 5x + 3\), find f(x + 1).
2x2 - x
2x2 - x + 10
4x2 + 3x + 2
4x2 + 3x + 12
Correct answer is A
\(f(x) = 2x^2 - 5x + 3\)
\(f(x + 1) = 2(x + 1)^2 - 5(x + 1) + 3\)
= \(2(x^2 + 2x + 1) - 5x - 5 + 3\)
= \(2x^2 + 4x + 2 - 5x - 2\)
= \(2x^2 - x\)