Question

Use the the factor theorem to determine wether the first polynomial is a factor of the second. X-3; 2x^2-4x+30

Answer 1

Given the polynomial function


`P(x)=2 x^(2) -4x+30`

If (x-3) is a factor of P(x), then


`P(x)=2 x^(2) -4x+30=(x-3)*Q(x)`, for some polynomial Q of 1st degree,

Then according to the factor theorem P(3)=0, because P(3)=(3-3)Q(x)=0*Q(3)=0.

Check


`P(3)=2 (3)^(2) -4(3)+30=18-12+30=36`≠0


we see that P(3) is not 0, so (x-3) is not a factor of P(x).


Answer: no