Question

Check whether the polynomial p(x)=4x³+4x²-x-1 is a multiply of (2x+1)Please give me own answer

Answer 1

Answer :

Given

• A polynomial p(x)=4x³+4x²-x-1
• And a factor (2x+1)

Find :

• Whether (2x+1) is a factor of p(x)=4x³+4x²-x-1 or not.

Solution :

We have the polynomial,

• p(x)=4x³+4x²-x-1

And a factor

• (2x+1)

◆Step by step explanation:

• Put 2x + 1 = 0
• 2x = 0 - 1
• x = $\dfrac{-1}{2}$

Putting $\dfrac{-1}{2}$ in the given polynomial :-

= 4x³+4x²-x-1

= (4× $\dfrac{-1}{2}$)³+(4× $\dfrac{-1}{2}$)²- $\dfrac{-1}{2}$-1

= (4 ×$\dfrac{-1}{8}$)+(4 ×$\dfrac{1}{4}$)- $\dfrac{-1}{2}$-1

= $\dfrac{-1}{2}$+1- $\dfrac{-1-2}{2}$

= $\dfrac{1}{2}$-( $\dfrac{-3}{2}$)

= $\dfrac{1+3}{2}$[/tex]

= $\dfrac{4}{2}$[/tex]

= 2

As 2 is not equal to 0 thus (2x+1) is not a factor of p(x)=4x³+4x²-x-1.

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