Question

Use the Remainder Theorem, find the remainder when 4x3 - 3x2 + 2x - 4 is divided by x + 1.​

Answer 1

Step-by-step explanation:

Let p(x) = 4x³ - 3x² + 2x - 4,

x + 1=0,

then

x = -1

Remainder= p(-1) = 4(-1)³ - 3(-1)² + 2(-1) - 4,

= -4 - 3 - 2 - 4,

= -13

Answer 2

Concept:

The remainder theorem states that if we divide a polynomial P(x) by a factor ( x – a), then the remainder obtained is p(a).

Given:

We have,

Polynomial  4x³ - 3x² + 2x - 4

And,

Factor (x + 1).

Find:

We are asked to find the remainder.

Solution:

We have,

Polynomial  4x³ - 3x² + 2x - 4

And,

Factor (x + 1),

So,

Let,

x + 1 =

we get,

x = -1

Now,

According to the Remainder Theorem putting this value in the given polynomial,

i.e.

p(x) =  4x³ - 3x² + 2x - 4

So,

p(-1) = 4(-1)³ - 3(-1)² + 2(-1) - 4

On solving we get,

p(-1) = - 4 - 3 - 2 - 4

i.e.

p(-1) = - 13,

i.e.

p(a) = -13

So, Remainder = -13

Hence, the remainder is -13.

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