Question

The expression 4x^3-6x² +x-6 leaves
remainders 0 and 30 when divided by
(x+1) and (2x-3) respectively. calculate
the values of b and c​

Answer 1

Step-by-step explanation:

Let f(x) = 4x3 − bx2 + x − c It is given that when f(x) is divided by (x + 1), the remainder is 0. f(− 1) = 0 4(− 1)3 − b(− 1)2 + (− 1) − c = 0 − 4 − b − 1 − c = 0 b + c + 5 = 0 ...(i) It is given that when f(x) is divided by (2x − 3), the remainder is 30. Multiplying (i) by 4 and subtracting it from (ii), we get, 5b + 40 = 0 b = − 8 Substituting the value of b in (i), we get, c = − 5 + 8 = 3 Therefore, Let f(x) = 4x3 − bx2 + x − 3 Now, for x = − 1, we get, f(x) = f(−1) = 4(− 1)3 + 8(− 1)2 + (− 1) − 3 = − 4 + 8 − 1 − 3 = 0 Hence, (x + 1) is a factor of f(x). Read more on Sarthaks.com - https://www.sarthaks.com/149840/the-expression-4x-3-bx-2-x-c-leaves-remainders-and-30-when-divided-by-x-and-2x-respectively