Question

if (x-1) is a factor of p^2x^2 -3px+(3p-1),find the value of p,write the given expression in factored form

Answer 1

Hi,

Let f( x ) = p² x² - 3px + 3p - 1

If ( x - 1 ) is a factor of f( x ) , then

f( 1 ) = 0 ,

p² × 1² - 3p × 1 + 3p - 1 = 0

p² - 3p + 3p - 1 = 0

p² - 1 = 0

p² = 1

p = ± 1 ,

1 ) put p = 1 , in f ( x ) ,

x² - 3x + 3 - 1

= x² - 3x + 2

= x² - 1x - 2x + 2

= x( x - 1 ) - 2( x - 1 )

= ( x - 1 )( x - 2 )

I hope this helps you.

: )