Question

Find the remainder when f(x) = –2x3 + x2 - 4x + 1 is divided by x + 3.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The remainder when f(x) is divided by x + 3 would be 76.

What is remainder theorem for polynomials?

If there is a polynomial p(x), and a constant number 'a', then

$\dfrac{p(x)}{(x-a)} = g(x) + p(a)$

where g(x) is a factor of p(x).

We have been given a function;

$f(x) = -2x^3 + x^2 - 4x + 1$

We need to find the remainder when f(x) is divided by x + 3.

So, Let p(x) = x + 3

p(x) = 0

x + 3 = 0

x = -3

Substitute in the given function f(x);

$f(x) = -2x^3 + x^2 - 4x + 1\\\\f(-3) = -2(-3)^3 + (-3)^2 - 4(-3) + 1\\\\f(-3) = 54 + 9 + 12 + 1\\\\f(-3) = 76$

Thus, the remainder when f(x) is divided by x + 3 would be 76.

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