If one factor of 56x^4y^3-42x^2y^6 is 14x^2y3,what is the other factor
mahamad
To find the other factor, we can divide the given expression by the given factor using polynomial long division:
2x^2y^6
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14x^2y^3 | 56x^4y^3 - 42x^2y^6
- (56x^4y^3 - 42x^2y^6)
_______________
0
Since the remainder is zero, it means that 14x^2y^3 is indeed a factor of 56x^4y^3 - 42x^2y^6. Therefore, the other factor is the quotient obtained during the division process, which is 4x^2.
So, the other factor is 4x^2.
To find the other factor, we can perform polynomial division.
Let's divide 56x^4y^3 - 42x^2y^6 by 14x^2y^3:
_________________________
14x^2y^3 | 56x^4y^3 - 42x^2y^6
To start, we divide the first term of the dividend (56x^4y^3) by the first term of the divisor (14x^2y^3), which gives us 4x^2.
4x^2
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14x^2y^3 | 56x^4y^3 - 42x^2y^6
- 56x^4y^3 + 56x^2y^6
Next, we multiply the quotient we obtained (4x^2) by the entire divisor (14x^2y^3) and subtract it from the dividend:
4x^2
_________________________
14x^2y^3 | 56x^4y^3 - 42x^2y^6
- 56x^4y^3 + 56x^2y^6
_________________________
0
As we can see, the remainder is 0, which means that 14x^2y^3 is indeed a factor of 56x^4y^3 - 42x^2y^6.
Therefore, the other factor would be the quotient we obtained: 4x^2.
So, the other factor is 4x^2.