Answer:
1.) (2x - 1)(x + 1)
2.) a = 6 ; b = -1
4.a.) x = all rational numbers excluding (-2÷3)
4.b.) x = -1
4.c.) Yes. x = 1÷2
Step-by-step explanation:
E(x) = (2x - 1)² + (x - 2)(1 - 2x) F(x) = ax²-bx-2
F(1) = 5 ; F(-2) = 20
a-b=7 ; 4a+2b=22
3.Answer) Q(x) = 6x² + x - 2
= 6x² + 4x - 3x - 2
= (3x + 2)×(2x - 1)
Hence verified!
P(x) = E(x) ÷ Q(x)
= (x + 1)÷(3x + 2)
Here, x belongs to,
[tex]( - \infty \: to \: - 2 \div 3) union( - 2 \div 3 \: to \: \infty )[/tex]
Means, except x = -2÷3 , all real numbers are valid excluding complex numbers.
P(x) = (x + 1)÷(3x +2) = 0
= > x = -1
