Question

Given that x-3 is a factor of x³ -2x²-4x+3, what could x be?

a) x = 3
b) x = 6
c) x = 0
d) x = -3

Answer 1

To find out which value of x is correct given that x-3 is a factor of the polynomial x³ -2x²-4x+3, we substitute x with 3 and validate that it makes the polynomial equal to 0. Therefore, the correct value is a) x = 3.

Step-by-step explanation:

To find the value of x given that x-3 is a factor of x³ -2x²-4x+3, we can use the fact that for a polynomial f(x), if (x-k) is a factor, then f(k) = 0. In this case, substituting x with 3 (the value from the factor x-3), we get:

f(3) = 3³ -2(3)² - 4(3) + 3 = 27 - 18 - 12 + 3 = 0

Since we got a result of 0, x = 3 satisfies the equation x³ -2x²-4x+3 which confirms that x = 3 is a solution. Therefore, the answer is a) x = 3.