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What is the remainder when 2x cubed plus x minus 7 is divided by x plus 2 using the remainder theorem?
Using the remainder theorem:- The function of x becomes f(-2) because the divisor is x+2 Substitute -2 for x in the dividend: 2x3+x-7 When: f(-2) = 2(-2)3+(-2)-7 = -25 Then: -25 is the remainder
How can you find the remainder by using the remainder theorem?
The Remainder Theorem states that if you divide a polynomial ( f(x) ) by a linear divisor of the form ( x - c ), the remainder is simply ( f(c) ). To find the remainder, substitute the value ( c ) into the polynomial ( f(x) ) and calculate the result. The output will be the remainder of the division. This method significantly simplifies finding remainders without performing long division.
What is the remainder R when the polynomial p(x) is divided by (x - 2)?
The remainder ( R ) when a polynomial ( p(x) ) is divided by ( (x - 2) ) can be found using the Remainder Theorem. According to this theorem, the remainder is equal to ( p(2) ). Thus, to find ( R ), simply evaluate the polynomial at ( x = 2 ): ( R = p(2) ).
When the polynomial in P(x) is divided by (x plus a) the remainder equals P(a)?
When a polynomial ( P(x) ) is divided by ( (x + a) ), the remainder can be found using the Remainder Theorem. This theorem states that the remainder of the division of ( P(x) ) by ( (x - r) ) is equal to ( P(r) ). Therefore, when dividing by ( (x + a) ), which is equivalent to ( (x - (-a)) ), the remainder is ( P(-a) ), confirming that ( P(-a) ) is the value of the polynomial evaluated at ( -a ).
How can you tell if a binomial divides evenly into a polynomial?
Do the division, and see if there is a remainder.
What is the remainder when 2x cubed plus x minus 7 is divided by x plus 2 using the remainder theorem?
Using the remainder theorem:- The function of x becomes f(-2) because the divisor is x+2 Substitute -2 for x in the dividend: 2x3+x-7 When: f(-2) = 2(-2)3+(-2)-7 = -25 Then: -25 is the remainder
How can you find the remainder by using the remainder theorem?
The Remainder Theorem states that if you divide a polynomial ( f(x) ) by a linear divisor of the form ( x - c ), the remainder is simply ( f(c) ). To find the remainder, substitute the value ( c ) into the polynomial ( f(x) ) and calculate the result. The output will be the remainder of the division. This method significantly simplifies finding remainders without performing long division.
What is the remainder R when the polynomial p(x) is divided by (x - 2)?
The remainder ( R ) when a polynomial ( p(x) ) is divided by ( (x - 2) ) can be found using the Remainder Theorem. According to this theorem, the remainder is equal to ( p(2) ). Thus, to find ( R ), simply evaluate the polynomial at ( x = 2 ): ( R = p(2) ).
When the polynomial in P(x) is divided by (x plus a) the remainder equals P(a)?
When a polynomial ( P(x) ) is divided by ( (x + a) ), the remainder can be found using the Remainder Theorem. This theorem states that the remainder of the division of ( P(x) ) by ( (x - r) ) is equal to ( P(r) ). Therefore, when dividing by ( (x + a) ), which is equivalent to ( (x - (-a)) ), the remainder is ( P(-a) ), confirming that ( P(-a) ) is the value of the polynomial evaluated at ( -a ).
How can you tell if a binomial divides evenly into a polynomial?
Do the division, and see if there is a remainder.
What is the remainder thereom?
The remainder theorem states that if you divide a polynomial function by one of it's linier factors it's degree will be decreased by one. This theorem is often used to find the imaginary zeros of polynomial functions by reducing them to quadratics at which point they can be solved by using the quadratic formula.
Can the Chinese theorem solve a sudoku puzzle?
The Chinese Remainder Theorem (CRT) is not directly applicable for solving Sudoku puzzles. Sudoku relies on a grid-based logic system where numbers must be placed according to specific rules rather than modular arithmetic. However, some concepts from the CRT, like working with congruences, can theoretically inspire techniques for Sudoku solving, but they do not provide a direct solution method. Sudoku is typically solved using backtracking, constraint propagation, or other algorithmic approaches.
Can a theorem be proven using a corollary?
No, a corollary follows from a theorem that has been proven. Of course, a theorem can be proven using a corollary to a previous theorem.
The number you are thinking of is between 12 and 32 when you divide it by 5 it leaves a remainder of 1 when i divide it by 4 it leaves a remainder of2?
To find the number, we need to consider the remainders when the number is divided by 5 and 4. Let's denote the number as x. From the information given, we have two equations: x ≡ 1 (mod 5) and x ≡ 2 (mod 4). By solving these congruences simultaneously using the Chinese Remainder Theorem, we find that x ≡ 21 (mod 20). Therefore, the number you are thinking of is 21.
What statement to a theorem can be proven easily using the theorem?
A corollary.
What is the remainder when 4x cubed plus 6x squared plus 3x plus 2 is divided by 2x plus 3 showing your work by means of the remainder theorem?
Using the remainder theorem:- f(x) = 4x3+6x2+3x+2 f(x) becomes f(-3/2) or f(-1.5) because the divisor is 2x+3 f(-1.5) = 4(-1.5)3+6(-1.5)2+3(-1.5)+2 = -5/2 or -2.5 So the remainder is -2.5
Is a theorem a statement that can be easily proved using a corollary?
No. A corollary is a statement that can be easily proved using a theorem.
