Question

Check whether f(x) = 4x^3 + 4x^2 – 1x – 1 is a multiple of 2x + 1

Answer 1

Step-by-step explanation:

Given :-

f(x) = 4x^3 + 4x^2 – 1x – 1

To find :-

Check whether f(x) = 4x^3 + 4x^2 – 1x – 1 is a multiple of 2x + 1 ?

Solution :-

Given Polynomial is f(x) = 4x³ + 4x² - 1x -1

=> (4x³ + 4x²) - (1x + 1 )

=> 4x²(x+1) -1(x+1)

=> (x+1)(4x²-1)

=> (x+1)(2²x²-1²)

=> (x+1)[(2x)²-1²]

We know that

(a+b)(a-b)=a²-b²

Where , a= 2x and b = 1

=> (x+1)(2x+1)(2x-1)

=> (2x+1)[(x+1)(2x-1)]

So, We have

(2x+1) is the one of the factors of f(x)

f(x) = 4x³ + 4x² - 1x -1 = (2x+1)[(x+1)(2x-1)]

It is clear that

f(x) is a multiple of (2x+1)

Hance, Verified.

Answer:-

f(x) = 4x³+4x²-1x-1 is a multiple of 2x + 1.

Used Method:-

• Factorization method

Used formulae:-

• (a+b)(a-b)=a²-b²