Factor. A) x^2-4x+3 B)x^2+5x-24

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We have given

A. `x^2-4x+3`

factorise 3 as 3.1

`3=3xx1`

`x^2-(3+1)x+3`

`=x^2-3x-x+3`

`` `=x(x-3)-1(x-3)`

`=(x-3)(x-1)` ( brackets are equal so factor out )

`B. x^2+5x-24`

`we write 24=8xx3`

`x^2+(8-3)x-24` ,

in bracket we take minus because last term has minus sign.

`=x^2+8x-3x-24`

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

`=(x+8)(x-3)` (brackets are same so factor out)

`A)` `x^2-4x+3` find soluton of `x^2-4x+3=0`

`Delta= 16-4(3)=4>0` has two solution

`x=(4+-sqrt(4))/2=(4+-2)/2` `x_1=3` `x_2= 1`

The poliniom is decomponed in:

`(x-x_1)(x-x_2)= (x-1)(x-3)`

``

`B)` `x^2+5x-24=0`

`Delta= 25-4(-24)=121>0` Two real different solutions.

`x=(-5+-sqrt(121))/2=(-5+-11)/2`

`x_1=3` `x_2=-8`

`x^2+5x-24=(x-3)(x+8)`

A) `x^2-4x+3`

use the a x c method

find factors of the product (3) that add up to b (-4) which would be -1 and -3 plug them in as b

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

group

`(x^2-x)(-3x+3) `

factor out he greatest common factor

x(x-1) -3(x-1)

(x-3) (x-1)

x=3 x=1

B)x^2+5x-24

follow the same steps here

find factors of -24 that add up to b (5) which would be 8 and -3

plug them in as b

`x^2+8x-3x-24 `

group

`(x^2+8x)(-3x-24) `

x(x+8) -3(x+8)

(x-3)(x+8)

x=3 x=-8

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