Question

check x-1 is a factor of x3+3x2-x+2

Answer 1

ANSWER.

• (x - 1) is not a factor of x³ + 3x² - x + 2

SOLUTION.

Here,

→ f(x) = x³ + 3x² - x + 2

x - 1 is a factor of f(x) if and only if f(1) = 0

Calculate f(1) –

→ f(1) = (1)³ + 3 × (1)² - 1 + 2

= 1 + 3 - 1 + 2

= 5

As f(1) ≠ 0, therefore, x - 1 is not a factor of f(x).

LEARN MORE.

• Factor Theorem: If f(x) is a polynomial of degree n ≥ 1 and a is any real number, then (x - a) is a factor of f(x) if f(a) = 0.
• It is used when we have to factor out a polynomial of higher degree.