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) ).
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.
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 ).
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 ).
I assume you meant x^4 + 5x^2 +10x + 12. The remainder is 28
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.
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.
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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
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 ).
I assume you meant x^4 + 5x^2 +10x + 12. The remainder is 28
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.
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!
29
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2
0.0328
3.5