Question

Using remainder theorem find the remainder when 3x4 -4x3 -3x-1 is divided by x + 2.

Answer 1

Answer:

Question:-

Using remainder theorem find the remainder when 3x4 -4x3 -3x-1 is divided by x + 2.

Given:-

• Two polynomials
• $3 {x}^{4} - 4 {x}^{3} - 3x - 1$
• x+2

To find:-

The remainder of this polynomial

$\huge{\boxed{\green{\underline{\red{\mathbb{Solution:-♡•}}}}}}$

First understand the remainder theorem:-

Remainder Theorem: When a polynomial p(x) is divided by x-a, then remainder is given by p(a); i.e. value of polynomial at x = a .

Step 1

Find the value of x from x+2

x+2=0

x=-2

Step 2

Putting the value of x in p(x)

Let p(x) =

$3 {x}^{4} - 4 {x}^{3} - 3x - 1$

p(-2) =

$3 { (- 1)}^{4} - 4 { (- 1)}^{3} - 3( - 1) - 1$

$\mapsto \: 3(1) - 4( - 1) + 3 - 1$

$\mapsto \: 3 + 4 + 3 - 1$

$\mapsto \: 10 - 1$

$\mapsto \: 9$

Therefore the remainder of

$3 {x}^{4} - 4 {x}^{3} - 3x - 1$

is 9

Step-by-step explanation:

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