Question

Is x-4 a factor of x³-2x²+3x+1?

Answer 1

by using factor theorem ..

x - 4 = 0

x = 4

p(x ) = x³ - 2x²+ 3x + 1

p(4) = 4³ - 2(4)² + 3(4) + 1

=> 64 - 32 + 12 + 1

=> 77- 32 = 45it is not 0 so we can say that x - 4 is not the factor of given polinomial .

Answer 2

$x {}^{3} - 2x {}^{2} + 3x + 1$

to check x - 4 is a factor we need to put
x = 4 in the polynomial.

$(4) {}^{3} - 2(4) {}^{2} + 3(4) + 1$

= 64 - 32 + 12 + 1

= 45

Hence x - 4 is not satisfying the polynomial so x - 4 is not a factor.

Thanks