Examples of divisor in the following topics:
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- For example, find the quotient and the remainder of the division of x3−12x2−42, the dividend, by x−3, the divisor.
- Multiply the divisor by the result just obtained (the first term of the eventual quotient): $x^2 \cdot (x − 3) = x^3 − 3x^2$.
- For example, find the quotient and the remainder of the division of x3−12x2−42, the dividend, by x−3, the divisor.
- Divide the first term of the dividend by the highest term of the divisor (meaning the one with the highest power of x, which in this case is x): x3÷x=x2.
- Multiply the divisor by the result just obtained (the first term of the eventual quotient): $x^2 \cdot (x − 3) = x^3 − 3x^2$.
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- Polynomial long division functions similarly to long division, and if the division leaves no remainder, then the divisor is called a factor.
- So we write down a 3x2, multiply the divisor with this result and subtract this from the dividend:
- As multiplying any polynomial with the divisor 2x−4 gets us a polynomial of degree greater than 0, we cannot divide any further.
- This means that D(x)=d(x)q(x): the dividend is a multiple of the divisor, or the divisor is said to divide the dividend.
- We say that the divisor is a factor of the dividend.
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- It states that the remainder of a polynomial f(x) divided by a linear divisor (x−a) is equal to f(a).
- We start by writing down the coefficients from the dividend and the negative second coefficient of the divisor.
- Bring down the first coefficient and multiply it by the divisor.
- Then add the next column of coefficients, get the result and multiply that by the divisor to find the third coefficient −27:
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- If a0 and an are nonzero, then each rational solution x=p/q, where p and qare coprime integers (i.e. their greatest common divisor is 1), satisfies:
- Since any integer has only a finite number of divisors, the rational root theorem provides us with a finite number of candidates for rational roots.
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- This can be solved using the property that if x0 is a zero of a polynomial, then (x−x0) is a divisor of this polynomial and vice versa.
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- If the dividend and the divisor have the same sign, that is to say, the result is always positive.
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- Therefore, we use the cancellation method to simplify the numbers as much as possible, and then we multiply by the simplified reciprocal of the divisor, or denominator, fraction:
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- Recall the rule for dividing fractions: the dividend is multiplied by the reciprocal of the divisor.
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- The term "conversion factor" is the multiplier, not divisor, which yields the result.