Question

Is x – 3 a factor of the polynomial p(x) = 2x4 – 9x3 + 15x2 – 22x + 12, and for what reason?

A)Yes, because p(3) is equal to 0.
B)Yes, because p(–3) is equal to 0.
C)No, because p(3) is not equal to 0.
D)No, because p(–3) is not equal to 0.

Answer 1

Answer:

A

Step-by-step explanation:

Using the Factor theorem

If (x - h) is a factor of a polynomial p(x) then p(h) = 0

(x - 3) → h = 3, evaluate p(3)

p|(3) = 2$(3)^{4}$ - 9(3)³ + 15(3)² - 22(3) + 12

       = (2 × 81) - (9 × 27) + (15 × 9) - (22 × 3) + 12

       = 162 - 243 + 135 - 66 + 12 = 0

Since p(3) = 0 then (x - 3) is a factor of p(x)