Question

Please answer this question
(1) (2)

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Answer 1

$\sf{Answer}$

Step by step explanation:-

Given :-

To factorise the Quadratic equations

• x² - 7x + 12
• x² - 8x + 15

Solution:-

x² - 7x + 12

Finding factors :-

12 × 1 = 12

Sum of the factors should be -7 & product of factors should be 12

(1x ) (12x) = 12x²

(- 1 x)( - 12x) = 12x²

(2 x )( 6x) = 12 x²

(-2x ) (-6 x) = 12x²

(3 x ) (4x ) = 12 x²

(-3 x )( -4 x)= 12 x²

(4 x )( 3x )= 12 x²

(-4x ) (-3x) = 12 x²

(6x )( 2x) = 12 x²

(-6x )( -2x) = 12x²

(12x) ( 1 x)= 12 x²

( - 12 x) (-1 x)= 12 x²

Now ,

If u observe factors Sum should be -7x product should be 12 x²

-3 x+ (-4) x = -7 x

(-3)x (-4)x = 12x²

Split the middle term

x² - 7x + 12

x² - 3x -4x + 12

Take the common

x( x -3 ) -4 ( x -3)

( x -3 ) ( x -4 )

So, the factorised form of x² - 7x + 12 is (x -3) ( x-4)

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2) x² - 8x + 15

Finding factors

Here the sum should be -8x & product should be 15x²

(1x ) (15x) = 15x²

(-1 x ) (-15x) = 15 x²

(3 x )( 5x) = 15 x²

(-3 x )( -5 x)= 15 x²

(5x )(3x )= 15 x²

(-5x ) (-3x) = 15 x²

(-15x )(- 1x) = 15 x²

Now,

If u observe factors

-3 + (-5) = -3 x -5x = -8 x

-3x × -5x = 15x²

Splitting the middle term

x² - 8x + 15

x² - 3x - 5x + 15

Take common

x ( x -3 ) -5 ( x -3)

(x -3) ( x-5)

So, the factorised form of x² -8x +15 is (x-3)(x-5)

Answer 2

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