Question

pls do not spam ... i need the correct ans .... the polynomial q (x) = 4x ³ + 4x² -x-1 is a multipe of a) 2x +1 b) 3x-1 c) x+1 d) x-1​

Answer 1

Solution :

The given polynomial , q(x) is 4x³ + 4x² - x - 1

We have to find if it is a multiple of the following options -

(2x+1) , (3x-1) , (x+1) or (x-1)

q(x) = 4x³ + 4x² - x - 1

>> (4x³ - x) + (4x²-1)

>> x(4x²-1) + 1(4x²-1)

>> (x+1)(4x²-1)

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

Answer : It is a multiple of 2x+1 and x+1. ( A and C )

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Answer 2

Answer:

Given :-

$\bf \: {4x}^{3} + 4 {x}^{2} - x - 1$

To Find :-

Which of these are the multiple of the given equation

Solution :-

4x³ + 4x² - x - 1

4x³ - x + 4x² - 1

x(4x² - 1) + 4x² - 1

x(4x² - 1) + 1(4x² - 1)

(x + 1)(4x² - 1)

(x + 1)(4x² - 2x + 2x - 1)

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

(x + 1)(2x + 1)(2x - 1)

Henceforth,

x + 1, 2x + 1 and 2x - 1 are the factors