SOLUTION: True or False?
A number k is a root of P(x) if and only if the remainder, when dividing P(x) by x+k, equals zero.
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-> SOLUTION: True or False?
A number k is a root of P(x) if and only if the remainder, when dividing P(x) by x+k, equals zero.
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A number k is a root of P(x) if and only if the remainder, when dividing P(x) by x+k, equals zero. Found 2 solutions by math_tutor2020, ikleyn:Answer by math_tutor2020(3817) (Show Source):
A number k is a root of P(x) if and only if the remainder, when dividing P(x) by x+k, equals zero.
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As written in the post, the statement is FALSE.
The correct statement is THIS
A number k is a root of P(x) if and only if
the remainder, when dividing P(x) by x-k, equals zero.
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It is the Remainder Theorem.
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Theorem (the remainder theorem)
1. The remainder of division the polynomial by the binomial is equal to the value of the polynomial.
2. The binomial divides the polynomial if and only if the value of is the root of the polynomial , i.e. .
3. The binomial factors the polynomial if and only if the value of is the root of the polynomial , i.e. .
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