how to find factors through division?
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Answer:
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Step-by-step explanation:
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.
Answer:
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Step-by-step explanation:
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