Question

(i) Which identity can be used to find the factors of x^2- 6x + 9 and what are its factors

Answer 1

Answer:

3, 3

Step-by-step explanation:

First term= 1

Middle term= -6

Last term = 9

Multiplication of first and last term = 9

Take two middle terms such that it's addition is equal to its middle term and it's multiplication is same as the multiplication of first and last term.

x^2 - 6x + 9 = x^2 - 3x -3x + 9

= x (x - 3) -3 (x - 3)

= (x - 3) (x - 3)

1st factor :- x - 3 = 0. 2nd factor :- x - 3 = 0

x = 0 + 3. x = 0 + 3

x = 3. x = 3

Therefore, the factors are 3, 3.

Answer 2

Answer:

The identity that is supposed to be used is - $x^2+(a+b)x+ab = (x+a)(x+b)$ .

Here,

a = 3

b = 3

x = $x^2$

$\\x^2$ + ( 3 + 3 ) $x$ + 9

$x$ ( $x$ + 3 ) + 3 ( $x$ + 3)

( x + 3 ) ( x + 3 )