31.) it is given that f(x) = ax^(3) + bx² -3, where a and b are constants.
(a) when f(x) is divided by x - 1, the remainder is 0; when it is divided by
x+1, the remainder is -2. find the values of a and b.
(s3/q21
(b) find the remainder when f(x - 1) is divided by x - 1.
{i have found (a),the value of a and b ,which is a=1 b=2
with (b)

Step-by-step explanation:

look this solution and verify

remainder = - 3

Step-by-step explanation:

Expressing f(x) with a = 1 and b = 2 ← from (a), then

f(x) = x³ + 2x² - 3 and so

f(x - 1) = (x - 1)³ + 2(x - 1)² - 3 ← distributing factors

          = x³ - 3x² + 3x - 1 + 2x² - 4x + 2 - 3

          = x³ - x² - x - 2

Using remainder theorem to evaluate remainder

f(1) = 1³ - 1² - 1 - 2 = 1 - 1 -1 - 2 = - 3 ← remainder

step-by-step explanation:

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