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Is it false if a polynomial is divided by (x-a) and the remainder equals zero then (x-a) is a factor of the polynomial?
No, it’s true. It’s the same as saying if 60 is divided by 2 and the remainder equals zero (no remainder, so it divides perfectly), 2 is a factor of 60.
What else can I help you with?
If a polynomial is divided by (x-a) and the remainder equals zero then (x-a) is a factor of the polynomial?
false - apex
What numbers is a factor of 60 9 or 7 or 4 or 8?
4 is a factor since 60 divided by 4 is 15, the others are not. To see if it is a factor, just see if it 60 divided by that number has a remainder or not. If the remainder is 0, it is a factor, if the remainder is non-zero it is not.
A remainder of 1 or more in the process of doing synthetic division tells you that you have found a root or a factor of the polynomial?
False
Can A factor can be divided evenly into another number with no remainder?
Yes! Only factors of number N can be divided into N with no remainder (that is why they are factors).
A remainder of zero in the process of doing synthetic division tells you that you have found a root or a factor of the polynomial?
That is true.
If a polynomial is divided by (x-a) and the remainder equals zero then (x-a) is a factor of the polynomial?
false - apex
If a polynomial is divided by (x - a) and the remainder equals zero then (x - a) is a factor of the polynomial.?
Yes, that's correct. According to the Factor Theorem, if a polynomial ( P(x) ) is divided by ( (x - a) ) and the remainder is zero, then ( (x - a) ) is indeed a factor of the polynomial. This means that ( P(a) = 0 ), indicating that ( a ) is a root of the polynomial. Thus, the polynomial can be expressed as ( P(x) = (x - a)Q(x) ) for some polynomial ( Q(x) ).
What is an expression that completely divides a given polynomial?
An expression that completely divides a given polynomial without leaving a remainder is called a factor of the polynomial. This means that when the polynomial is divided by the factor, the result is another polynomial with no remainder. Factors of a polynomial can be found by using methods such as long division, synthetic division, or factoring techniques like grouping, GCF (greatest common factor), or special patterns.
What is the factor theorem?
In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem.The factor theorem states that a polynomial has a factor if and only if
Which binomial is a factor of the polynomial below?
To determine which binomial is a factor of a given polynomial, you can apply the Factor Theorem. According to this theorem, if you substitute a value ( c ) into the polynomial and it equals zero, then ( (x - c) ) is a factor. Alternatively, you can perform polynomial long division or synthetic division with the given binomials to see if any of them divides the polynomial without a remainder. If you provide the specific polynomial and the binomials you're considering, I can assist further.
What does factor theorem mean?
In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem.The factor theorem states that a polynomial has a factor if and only if
When dividing a polynomial F x by the binomial x - a a remainder not equal to zero tells you that x - a is not a of the polynomial?
factor
A remainder of zero in the process of doing synthetic division tells you that you have found a root of the polynomial function and a factor of the polynomial. A. True?
true
When a remainder of 1 or more in the process of doing synthetic division tells you that you have found a root of the polynomial function and a factor of the polynomial.?
The statement is not true.
When dividing the polynomial x3 4x2 5x 2 by x 2 the remainder is 0 making x 2 a factor?
Yes, if there is no remainder after division, the divisor is a factor.
The polynomial x - 2 is a factor of the polynomial Fx equals 5x2 - 6x plus 4?
False
When a polynomial is divided by one of its binomial factors what is the quotient called?
When a polynomial is divided by one of its binomial factors, the quotient is called the "reduced polynomial" or simply the "quotient polynomial." This resulting polynomial represents the original polynomial after removing the factor, and it retains the degree that is one less than the original polynomial.
