Question

for the polynomial x^3 - 4x^2 - 17x + 60, x - 3 is one of the factors.
what are the other two factors of this polynomial?
○ (x + 6)(x + 10)
○ (x - 5)(x + 4)
○ (x - 10)(x + 2)
○ (x + 20)(x + 3)

Explanation:

Step1: Divide the polynomial by \(x - 3\)

We use polynomial long division or synthetic division. Let's use synthetic division. The root is \(x = 3\), so we set up synthetic division with 3:

$$
LATEXBLOCK0
$$

So the quotient polynomial is \(x^2 - x - 20\).

Step2: Factor the quotient polynomial

We factor \(x^2 - x - 20\). We need two numbers that multiply to \(-20\) and add to \(-1\). The numbers are \(-5\) and \(4\), so \(x^2 - x - 20=(x - 5)(x + 4)\).

So the other two factors are \((x - 5)(x + 4)\), which is option B.

Answer:

B. \((x - 5)(x + 4)\)