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 y3−4xy+xy3−4y
(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
y3−4xy+xy3−4y
= \(y^3(1 + x) - 4y(1 + x)
(y3−4y)(1+x)=(y3(1+x)−4y(1+x))
∴ = y(1+x)(y+2)(y−2)
2(x - 9)
2(9 + x)
81 - x2
-2(x - 9)
Correct answer is D
324−4x22x+18 = 182−(2x)22x+18
= (18−2x)(18+2x)(2x+18)
18 - 2x = 2(9 - x)
or -2(x - 9)
Solve for a positive number x such that 2(x3−x2−2x)=1
4
3
2
1
Correct answer is C
2(x3−x2−2x)=1
x3−x2−2x=0
x(x2−x−2)=0
x2−x−2=0
(x+1)(x−2)=0
x = 2 is the positive answer.
If f(x)=2x2−5x+3, find f(x + 1).
2x2 - x
2x2 - x + 10
4x2 + 3x + 2
4x2 + 3x + 12
Correct answer is A
f(x)=2x2−5x+3
f(x+1)=2(x+1)2−5(x+1)+3
= 2(x2+2x+1)−5x−5+3
= 2x2+4x+2−5x−2
= 2x2−x