Question

Let f(x)=2x^2-x-1 and let g(x)=x-1 Which statement is true?​

Answer 1

Answer:

B is true

Step-by-step explanation:

given f(x) = 2x² - x - 1 and g(x) = x - 1

A

If x = - 1 is a root then f(- 1) = 0

f(- 1) = 2(- 1)² - (- 1) - 1 = 2 + 1 - 1 = 2 ≠ 0 ← False

B

If (x - 1) is a factor then x = 1 is a root and f(1) = 0

f(1) = 2(1)² - 1 - 1 = 2 - 1 - 1 = 0

⇒ g(x) = x - 1 is a factor of f(x) ← True

C

If x = 2 is a root then f(2) = 0

f(2) = 2(2)² - 2 - 1 = 8 - 3 = 5 ≠ 0 ← False

D

$\frac{x2x^2-x-1}{x-1}$ = $\frac{(2x+1)(x-1)}{x-1}$

Cancel the factor (x - 1) on the numerator/ denominator, leaving

$\frac{f(x)}{g(x)}$ = 2x + 1 with remainder 0 ≠ 2 ← False