Question

if x+1 is a factor of the polynomial x^3+1 then find the other factor​

Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:

☛Given :

Polynomial expression : 2x^2 - x - 1

⚝Required to find :

Other factor

✯Explanation✯ :

First we have to use factor theorem and check whether x - 1 is the factor of the polynomial or not .

Then, we have to divide the polynomial expression with x - 1 in the procedure of long division .

After dividing the polynomial the remainder will be zero and the quotient becomes a factor .

This quotient in some case needs to be factorised but in other cases it is need not .

The case is when the given polynomial expression is an Cubic Expression .

☞ Solution :

p(x) = 2x^2 - x - 1

Let x - 1 is a factor

x - 1 = 0

x = 1

p(1) = 2(1)^2 - 1 -1

= 2 - 1 - 1

= 2 - 2

= 0

Hence, x - 1 is a factor .

Quotient is 2x + 1

Now equal this value with 0

2x + 1 = 0

2x = - 1

This , value when substituted in the expression will gives the answer as zero . However, it is a factor .

Hence , The other factor is 2x + 1 .

☛Given :

Polynomial expression : 2x^2 - x - 1

⚝Required to find :

Other factor

✯Explanation✯ :

In this method we have to factorise the given polynomial expression this is because ;

Factorisation is method of dividing the polynomial expression into it's factors .

Similarly, when the factors are multipled they give back the polynomial expression .

Here, the method used in factorisation is ;

First we have to multiply the coefficient of the first term with the last term then we have to Split the middle term such that their product should be equal to the last term and the sum should be equal to the middle term .

☞ Solution :

See the result

We have 2 factors .

In the question he had given one factor .

Hence, the other factor is ( 2x + 1 ) .