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What is the remainder when 2 is synthetically divided into the polynomial?
To find the remainder when a polynomial is divided by (x - 2) using synthetic division, we substitute (2) into the polynomial. The remainder is the value of the polynomial evaluated at (x = 2). If you provide the specific polynomial, I can calculate the remainder for you.
What is the remainder when x3 x2 5x 6 is divided by x 2?
To find the remainder when the polynomial ( x^3 + x^2 + 5x + 6 ) is divided by ( x^2 ), we can use polynomial long division or simply evaluate the polynomial at the roots of ( x^2 = 0 ), which are ( x = 0 ) and ( x = 0 ). The remainder will be a polynomial of degree less than 2, in the form ( ax + b ). Substituting ( x = 0 ) into the original polynomial gives ( 6 ) for the constant term, and substituting gives the linear term ( 5 \cdot 0 = 0 ). Thus, the remainder is ( 5x + 6 ).
What is the remainder when (x3 1) is divided by (x2 x 1)?
To find the remainder when ( x^3 + 1 ) is divided by ( x^2 + x + 1 ), we can use polynomial long division. Upon performing the division, we find that the remainder is a polynomial of degree less than the divisor, which is ( x^2 + x + 1 ). The result shows that the remainder is ( -x + 1 ). Thus, the remainder when ( x^3 + 1 ) is divided by ( x^2 + x + 1 ) is ( -x + 1 ).
What is the remainder when the polynomial x4 5x2 10x 12 is divided by x plus 2?
I assume you meant x^4 + 5x^2 +10x + 12. The remainder is 28
What is the quotient in polynomial form?
The quotient in polynomial form refers to the result obtained when one polynomial is divided by another polynomial using polynomial long division or synthetic division. It expresses the division result as a polynomial, which may include a remainder expressed as a fraction of the divisor. The quotient can help simplify expressions and solve polynomial equations. For example, dividing (x^3 + 2x^2 + x + 1) by (x + 1) yields a quotient of (x^2 + x) with a remainder.
What is the remainder when 2 is synthetically divided into the polynomial?
To find the remainder when a polynomial is divided by (x - 2) using synthetic division, we substitute (2) into the polynomial. The remainder is the value of the polynomial evaluated at (x = 2). If you provide the specific polynomial, I can calculate the remainder for you.
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 is the remainder when 2 is synthetically divided into the polynomial -3x2 plus 7x-9?
-7
What do we use the polynomial remainder theorem for?
If a polynomial is divided by x - c, we can use the Remainder theorem to evaluate the polynomial at c.The Remainder theorem:If the polynomial f(x) is divided by x - c, then the remainder is f(c).Example:Given f(x) = x^3 - 4x^2 + 5x + 3, use the remainder theorem to find f(2).Solution:By the remainder theorem, if f(x) is divided by x - 2, then the remainder is f(2).We can use the synthetic division to divide.2] 1 -4 5 32 -4 2__________1 -2 1 5The remainder is 5, so f(2) = 5Check:f(x) = x^3 - 4x^2 + 5x + 3f(2) = (2)^3 - 4(2)^2 + 5(2) + 3 = 8 - 16 + 10 + 3 = 5
What is the remainder when x3 x2 5x 6 is divided by x 2?
To find the remainder when the polynomial ( x^3 + x^2 + 5x + 6 ) is divided by ( x^2 ), we can use polynomial long division or simply evaluate the polynomial at the roots of ( x^2 = 0 ), which are ( x = 0 ) and ( x = 0 ). The remainder will be a polynomial of degree less than 2, in the form ( ax + b ). Substituting ( x = 0 ) into the original polynomial gives ( 6 ) for the constant term, and substituting gives the linear term ( 5 \cdot 0 = 0 ). Thus, the remainder is ( 5x + 6 ).
What is the remainder when (x3 1) is divided by (x2 x 1)?
To find the remainder when ( x^3 + 1 ) is divided by ( x^2 + x + 1 ), we can use polynomial long division. Upon performing the division, we find that the remainder is a polynomial of degree less than the divisor, which is ( x^2 + x + 1 ). The result shows that the remainder is ( -x + 1 ). Thus, the remainder when ( x^3 + 1 ) is divided by ( x^2 + x + 1 ) is ( -x + 1 ).
What is the remainder when the polynomial x4 5x2 10x 12 is divided by x plus 2?
I assume you meant x^4 + 5x^2 +10x + 12. The remainder is 28
What is the quotient in polynomial form?
The quotient in polynomial form refers to the result obtained when one polynomial is divided by another polynomial using polynomial long division or synthetic division. It expresses the division result as a polynomial, which may include a remainder expressed as a fraction of the divisor. The quotient can help simplify expressions and solve polynomial equations. For example, dividing (x^3 + 2x^2 + x + 1) by (x + 1) yields a quotient of (x^2 + x) with a remainder.
What is polynomial division?
That means that you divide one polynomial by another polynomial. Basically, if you have polynomials "A" and "B", you look for a polynomial "C" and a remainder "R", such that: B x C + R = A ... such that the remainder has a lower degree than polynomial "B", the polynomial by which you are dividing. For example, if you divide by a polynomial of degree 3, the remainder must be of degree 2 or less.
What is the remainder when 2 is synthetically divided into the polynomial -3x2 plus 7x minus 9?
Oh, what a happy little question! Let's gently divide 2 into the polynomial -3x^2 + 7x - 9. When we do that, we find that the remainder is -6x - 21. Just remember, there are no mistakes, only happy little accidents in math!
What number divided by 2 has a remainder 1 divided by 3 has a remainder 2 divided by four has a remainder 3 divided by 5 has a remainder 4?
29
What number as a remainder of 1 when divided by 2 as a remainder of 2 when divided by 3 as a remainder of 3 when divided by 4 and a remainder of 4 when divided by 5?
59
