Questions: Question 11 Choose the correct answer. Factor (f(x)) into linear factors. [ f(x)=x^3-3 x^2-49 x+147 ] (A) (f(x)=(x-7)(x-3)(x+3)) (B) (f(x)=(x-7)(x+3)(x+7)) (C) (f(x)=x(x-7)(x-3)) (D) (f(x)=(x-7)(x-3)(x+7))

Solution Steps

To factor the polynomial \( f(x) = x^3 - 3x^2 - 49x + 147 \) into linear factors, we can use the Rational Root Theorem to find potential rational roots. Once we find a root, we can use polynomial division to factor out the corresponding linear factor and repeat the process for the resulting polynomial.

We start with the polynomial given by \[ f(x) = x^3 - 3x^2 - 49x + 147. \]

Using the Rational Root Theorem, we find the roots of the polynomial. The roots are \[ x = -7, \quad x = 3, \quad x = 7. \]

Using the roots, we can express the polynomial in its factored form as \[ f(x) = (x - 7)(x - 3)(x + 7). \]

Final Answer