Question

Use the remainder Theorem to find which of the following is a factor of 2x³ + 3x² − 5x – 6. 

(i) x + 1 

(ii) 2x – 1 

(iii) x + 2

(iv) (3x − 2)

(v) (2x − 3)

Answer 1

By remainder theorem we know that when a polynomial f (x) is divided by x - a, then the remainder is f(a).

Let f(x) = 2x³ + 3x² − 5x − 6

(i) f (−1) = 2(−1)³ + 3(−1)² − 5(−1) − 6 = −2 + 3 + 5 − 6 = 0

Thus, (x + 1) is a factor of the polynomial f(x).

Thus, (2x − 1) is not a factor of the polynomial f(x).

(iii) f (−2) = 2(−2)³ + 3(−2)² − 5(−2) − 6 = −16 + 12 + 10 − 6 = 0

Thus, (x + 2) is a factor of the polynomial f(x).

Thus, (3x − 2) is not a factor of the polynomial f (x).

Thus, (2x − 3) is a factor of the polynomial f(x).