Question

the remainder therom 2x^3 +3x^2-5x-6 divided by x+1​

Answer 1

Answer:

Step-by-step explanation:

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) = 2 x 3 + 3 x 2 − 5 x − 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, (2 x − 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, (3 x − 2) is not a factor of the polynomial f (x). Thus, (2 x − 3) is a factor of the polynomial f(x).

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