Question

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

f(x) = 4x3 + 23x² – 34x +7; k= 1
f(x) = (Factor completely.)

Answer 1

Explanation:

step 1. if k is a zero then (x - 1) is a factor of 4x^3 + 23x^2 - 34x + 7.

step 2. we "can" use long division but synthetic division is easier!

step 3. 1 4 23 -34 7

4. 4. 27. -7.

4 27. -7. 0 (must get 0)

step 4. so the factors are (x - 1)(4x^2 + 27x - 7).

step 5. please note if you multiply these factors together you will get the original polynomial!