Question

Q. 25 Check whether (x+1) is a factor of 2x²-x-1​

Answer 1

Answer:

To check this we have to divide the the factor that is x+1 by the given polynomial that is

${2x}^{2} - x - 1$

We can perform this division by the following method which is shown in attachment and can see whether it is factor of the given polynomial or not .

On dividing by this factor if we get the remainder is equal to zero then we will conclude that it is a factor and if not get remainder as zero then it is not the factor of given polynomial .

Answer 2

$\LARGE{\mathfrak{\underline{\underline{\pink{AnSwEr:-}}}}}$

See the attachment.

$\Large{\mathfrak{\underline{\underline{\green{Explanation:-}}}}}$

➭ (X + 1) is not a factor of 2x² - x - 1

Because Reminder ≠ 0 and it is 2 .

$\rule{200}{2}$

If on diving the given factor we get reminder as 0 we can say that the number is divisible by the given polynomial.

$\rule{200}{2}$

Another Way :-

x -1 = 0

⇒ x = -1

Put Value of x in equation

We have,

2(-1)² - (-1) -1

⇒ 2(1) + 1 - 1

⇒ 2

So, 2x² - x - 1 is not divisible by (x+1)

Because it is ≠ 0

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Hope it helps.