Question

P(x) has factors (x-2), (x+1), and (x-3). Decide if there is only one polynomial that has these factors. Justify your conclusions

Answer 1

P(x)= x³ +2x² -5x -6

It's only the above polynomial that have the factors (x-2), (x+1), and (x-3).

Explanation:

P(x) has factors of (x-2), (x+1), and (x-3)

Let's determine the polynomial p(x)

(x-2) (x+1) (x-3)= (x² +x-2x-2)(x-3)

(x-2)(x+1)(x-3)= (x²-x-2)(x+3)

(x²-x-2)(x+3)= x³ + 3x² -x² -3x -2x -6

(x²-x-2)(x+3)= x³ +2x² -5x -6

P(x)= x³ +2x² -5x -6

As we can see the polynomial p(x) was gotten from the multiplication of the the three factors.

So it's only the polynomial that has these factors.

The polynomial that has the factors

(x-2), (x+1), and (x-3) is polynomial p(x) only.