Question

factorize y^3+y^2-y-1(by division method and who will ans quickly and good ans i will mark him or her as brainliest)​

Answer 1

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In factorisation by simple division method, we first break the polynomial into its direct factors. For example, if we divide 8y3+7y2+6y by 2y, we first break the polynomial into its basic factors, i.e : 2y(4y) 2+ 2y (7/2 *y) + 2y(3)

Next, we write the common factor separately, where we get: 2y { 4y2+(7/2y) + 3}. In the last step, we divide the expression as asked in the question i.e: 2y {4y2+(7/2y) + 3} / 2y. The answer to this shall be: 4y2+ (7/2y) + 3

Example 1: Divide 16(x2yz + xy2z+xyz2) by 4xyz

Solution : 2×2×2×2× [(x×x×y×z) + (x×y×y×z) + (x×y×z×z)]

= 2×2×2×2× {x×y×z (x+y+z)}

= 16xyz (x+y+z)

Now divide the polynomial as given in the question:

= 4*4xyz (x+y+z) / 4xyz

= 4(x+y+z)

Finding Factors: The Long Division Way

While finding factors of a polynomial using division method we need to accurately follow the steps given underneath:

Firstly, we arrange the polynomials in descending order. Wherever a term is missing we replace it with a zero ( (0). For example: Take a polynomial : x3+6x2+12+3x / x+3. Here, we first rearrange the polynomial as x3+6x2+3x+12

When we start the division of a polynomial, our first target is the first term of the polynomial. We divide the dividend’s first term with the first term of the divisor. From here we get our first quotient:

x+3 |x3+6x2+12| x2 ( x3 ÷ x = x2)

Then we multiply this quotient with the divisor, in the example we get:

(x+3) × x2 = x3+3x2

We now subtract the product from the dividend, like we do in the normal division calculations. Whatever the difference we get shall be our next dividend.

x+3 |x3+6x2+12| x2 gives x3 + 3x2

Bring down the next term and whatever the answer we get here is again divided by the divisor in a similar manner. We repeat the steps until we get a remainder which is lower than the divisor or is a Zero.

Now, if the remainder is a zero, we come to the conclusion that the divisor is the factor of the given polynomial.

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Answer 2

First find the value of y by hit & trial method such as in y = 1, that's why y-1 is a factor of y^3+y^2-y-1, & then divide it as given in photo

Explanation

Hope it helps