Question

(x–1) is a factor of p(x)=x⁴–2x³+3x–2,Examine the validity of the given statement.

Answer 1

(x - 1) is a factor of P(x) = x⁴ - 2x³ + 3x - 2

means, x = 1 is a root of P(x) = x⁴ - 2x³ + 3x - 2.

P(1) = 1⁴ - 2(1)³ + 3(1) - 2

P(1) = 1 - 2 + 3 - 2

P(1) = 4 - 4 = 0

we get, P(1) = 0 hence, the given statement is correct that (x - 1) is a factor of p(x)=x⁴–2x³+3x–2.

Answer 2

Hi ,

p( x ) = x⁴ - 2x³ + 3x - 2 ,

and g( x ) = x - 1 ,

The zero of g( x ) is 1 ,

Then p( 1 ) = 1⁴ - 2 × 1³ + 3 × 1 - 2

= 1 - 2 + 3 - 2

= 4 - 4

= 0

So , by Factor Theorem , ( x - 1 ) is a factor

of p( x ).

I hope this helps you

: )