if (f(-5)=0), what are all the factors of the function (f(x)=x^{3}-19x + 30)? use the remainder…

if (f(-5)=0), what are all the factors of the function (f(x)=x^{3}-19x + 30)? use the remainder theorem.\n((x - 2)(x + 5)(x - 3)\n(x + 2)(x - 5)(x + 3)\n(x - 2)(x + 5)\n(x + 2)(x - 5))

if (f(-5)=0), what are all the factors of the function (f(x)=x^{3}-19x + 30)? use the remainder theorem.\n((x - 2)(x + 5)(x - 3)\n(x + 2)(x - 5)(x + 3)\n(x - 2)(x + 5)\n(x + 2)(x - 5))

Answer

Explanation:

Step1: Apply Remainder Theorem

Since (f(- 5)=0), by the Remainder Theorem, ((x + 5)) is a factor of (f(x)=x^{3}-19x + 30).

Step2: Perform polynomial long - division

Divide (x^{3}-19x + 30) by (x + 5). Using polynomial long - division: (x^{3}-19x + 30=(x + 5)(x^{2}-5x + 6)).

Step3: Factor the quadratic

Factor (x^{2}-5x + 6) as ((x-2)(x - 3)) (since (x^{2}-5x + 6=x^{2}-2x-3x + 6=x(x - 2)-3(x - 2)=(x - 2)(x - 3))).

Step4: Write the complete factorization

So (f(x)=(x + 5)(x - 2)(x - 3)).

Answer:

A. ((x - 2)(x + 5)(x - 3))