Question

slove the question number 1,2​

Answer 1

1.

0.(61)bar + 0.(52)bar

=> 61/99 + 52/99

=> (61 + 52)/99

=> 113/99

=> (99 + 14)/99

=> 1 + 14/99

=> 1.(14)bar

Therefore, 0.(61)bar + 0.(52)bar = 1.(14)bar

2.

p(x) = x^3 - 3x^2 - x + 3.

Using factor theorem.

Consider the coefficient of x^0, i.e., 3.

3 = 1 × 3

Let x = 1.

p(1) = (1)^3 - 3(1)^2 - 1 + 3

p(1) = 1 - 3 - 1 + 3

p(1) = 0

Therefore, (x - 1) is a factor.

So,

x^3 - 3x^2 - x + 3

=> x^3 - x^2 - 2x^2 + 2x - 3x + 3

=> x^2(x - 1) - 2x(x - 1) - 3(x - 1)

=> (x - 1)(x^2 - 2x - 3)

=> (x - 1)(x^2 - 3x + x - 3)

=> (x - 1)(x(x - 3) + 1(x - 3))

=> (x - 1)(x + 1)(x - 3)

Hence factorized!

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