what is meant by remainder theorem
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♠hey there..!!
here is ur ans...⚡⚡
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⚫Theorem
Everyone loves to find a shortcut whether it involves driving directions or some other type of long task. Discovering a quicker and more efficient way to arrive at the same end point makes you feel good since you've most likely saved time, effort, and/or money. Math is filled with these types of shortcuts and one of the more useful ones is the remainder theorem.
The remainder theorem states that when a polynomial, f(x), is divided by a linear polynomial , x - a, the remainder of that division will be equivalent to f(a). In other words, if you want to evaluate the function f(x) for a given number, a, you can divide that function by x - a and your remainder will be equal to f(a).
It should be noted that the remainder theorem only works when a function is divided by a linear polynomial, which is of the form x + number or x - number. How does the remainder theorem save you time? Let's find out.
⚫How the Remainder Theorem Works
The remainder theorem is especially useful when it is paired with synthetic division. If you remember, synthetic division is an alternate method to quickly and easily divide polynomials instead of using long division. Also remember that in synthetic division, the number in the bottom row in the last column on the right is the remainder. Thus, rather than plugging a value in and using order of operations, you can use synthetic division as a way to evaluate a polynomial for a given value.
Additionally, synthetic division and the remainder theorem can be used to determine if a value is a zero of a function. Hopefully, you remember that a zero of a function, by definition, is any point c, where f(c) = 0. Therefore, if you find a remainder of zero after performing synthetic division, the number listed out front, referred to as a in the definition above, evaluates to zero or f(a) = 0.
Note that you can use long division instead of synthetic division, but it's almost always faster and easier to use synthetic division
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hope it helps‼✌✌
#Be brainly
here is ur ans...⚡⚡
=============================
⚫Theorem
Everyone loves to find a shortcut whether it involves driving directions or some other type of long task. Discovering a quicker and more efficient way to arrive at the same end point makes you feel good since you've most likely saved time, effort, and/or money. Math is filled with these types of shortcuts and one of the more useful ones is the remainder theorem.
The remainder theorem states that when a polynomial, f(x), is divided by a linear polynomial , x - a, the remainder of that division will be equivalent to f(a). In other words, if you want to evaluate the function f(x) for a given number, a, you can divide that function by x - a and your remainder will be equal to f(a).
It should be noted that the remainder theorem only works when a function is divided by a linear polynomial, which is of the form x + number or x - number. How does the remainder theorem save you time? Let's find out.
⚫How the Remainder Theorem Works
The remainder theorem is especially useful when it is paired with synthetic division. If you remember, synthetic division is an alternate method to quickly and easily divide polynomials instead of using long division. Also remember that in synthetic division, the number in the bottom row in the last column on the right is the remainder. Thus, rather than plugging a value in and using order of operations, you can use synthetic division as a way to evaluate a polynomial for a given value.
Additionally, synthetic division and the remainder theorem can be used to determine if a value is a zero of a function. Hopefully, you remember that a zero of a function, by definition, is any point c, where f(c) = 0. Therefore, if you find a remainder of zero after performing synthetic division, the number listed out front, referred to as a in the definition above, evaluates to zero or f(a) = 0.
Note that you can use long division instead of synthetic division, but it's almost always faster and easier to use synthetic division
=============================
hope it helps‼✌✌
#Be brainly
Answered by
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In algebra, the polynomial remainder theorem or little Bézout's theorem is an application of Euclidean division of polynomials. It states that theremainder of the division of a polynomial by a linear polynomial is equal to. In particular, is a divisor of if and only if a property known as the factor theorem.
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