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

Answer 1

Answer:

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).Read more on Sarthaks.com - https://www.sarthaks.com/149566/use-the-remainder-theorem-to-find-which-of-the-following-is-a-factor-of-2x-3-3x-2-5x-6

Answer 2

Step-by-step explanation:

therefore ,

( x+1 ) is a factor of 2x3 + 3x2 – 5x – 6

I hope it helps u