Question

P(x). g(x). q(x). r(x)
x-1. 3
x-3. 5
(x-1)(x-3). ?
15 is not a right answer

Answer 1

(i) Let us assume the division of 6x2 + 2x + 2 by 2

Here, p(x) = 6x2 + 2x + 2

g(x) = 2

q(x) = 3x2 + x + 1

r(x) = 0

Degree of p(x) and q(x) is same i.e. 2.

Checking for division algorithm,

p(x) = g(x) × q(x) + r(x)

Or, 6x2 + 2x + 2 = 2x (3x2 + x + 1)

Hence, division algorithm is satisfied.

(ii) Let us assume the division of x3+ x by x2,

Here, p(x) = x3 + x

g(x) = x2

q(x) = x and r(x) = x

Clearly, the degree of q(x) and r(x) is the same i.e., 1.

Checking for division algorithm,

p(x) = g(x) × q(x) + r(x)

x3 + x = (x2 ) × x + x

x3 + x = x3 + x

Thus, the division algorithm is satisfied.

(iii) Let us assume the division of x3+ 1 by x2.

Here, p(x) = x3 + 1

g(x) = x2

q(x) = x and r(x) = 1

Clearly, the degree of r(x) is 0.

Checking for division algorithm,

p(x) = g(x) × q(x) + r(x)

x3 + 1 = (x2 ) × x + 1

x3 + 1 = x3 + 1

Thus, the division algorithm is satisfied.

Answer 2

♣️ HEY MATE ♣️

(x-1)(x-3) = X²-3x-x+3

= x²-(3-1)X+3== x²-(2)X+3

== x²-2x+3... is the.... ...