Question

Find the GCD of (x²-9x+20) and (x⁴-256)​

Answer 1

Question given :

• We need to find the GCD i.e the greatest common divisor of x² - 9x + 20 and x⁴ - 256

Given :

• Polynomials x² - 9x + 20 and x⁴ - 256

To find :

• Greatest common divisor

Solution :

First take the polynomial x² - 9x + 20 ,

= x² - 9x + 20

= x² - 4x - 5x + 20

= x( x - 4 ) - 5( x - 4 )

= ( x - 4 ) × ( x - 5 )

Second polynomial x⁴ - 256 ,

= x⁴ - 256

= (x²)² - (16)²

Use identity a² - b² = ( a - b )( a + b )

= ( x² - 16 ) ( x² + 16 )

= ( x - 4 )( x + 4 )( x² + 16 )

We have ( x - 4 ) as common therefore it is the Highest common factor or the greatest common divisor of these polynomials .