Question

Factor (x) into linear factors given that k is a zero of f(x)

Answer 1

Factored form (linear): (4x+3)(x-3)(x-5)

Explanation:

Using long division and factoring, we can find the answer. Since the root/zero of 5 is given already, we can change this into a factor of (x - 5) as 5 is a root.

Step 1: Long division. Divide f(x) by (x-5)

Once you do long division, you should have left over (x-5)(4x²+9x-9)

Step 2: Factor the quadratic

Since you can't do gcf, you have to leave the 4x as a factor. Once you factor out the quadratic, you should get the answer:

(x-5)(4x+3)(x-3)

Step 3: Rearrange (Optional)

(4x+3)(x-3)(x-5)