Question

factorise the following

(x²-3x)² – 5( x² – 3x) – 50​

Answer 1

Step-by-step explanation:

first let's a= x²-3x

then ,

a²-5a-50

= a²-10a+5a-50

= a(a-10) +5(a-10)

= (a+5)(a-10)

so

after putting value of a in solution

the factrization= (x²-3x+5)(x²-3x+3)

Answer 2

(x²-3x)² – 5( x² – 3x) – 50

⇒ Here, let (x² -3x) = y.

= (x²-3x)² – 5( x² – 3x) – 50

= y² - 5y - 50 ㅤ...[∵x²-3x = y]

= y² - (10-5)y - 50

= y² -10y + 5y -50

= y ( y-10 ) + 5 ( y-10 )

= (y-10) (y+5)

So, y = 10 or y = -5

Now,

⇒ When y = 10,

x² - 3x = 10

x² - 3x -10 = 0

Using quadratic formula,

x = -b ± √(b²-4ac) / 2a

x = 3 ± √(-3)² - 4(1)(-10) / 2(1)

x = 3 ± √(9+40) /2

x = 3 ± √(49)/2

x = 3 ± 7 /2

⇒ When y = -5,

x² - 3x = -5

x² - 3x +5 = 0

Using quadratic formula,

x = -b ± √(b²-4ac) / 2a

x = 3 ± √[(-3)² - 4(1)(5)] / 2(1)

x = 3 ± √(9-20) /2

x = 3 ± √(-11) /2