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What is a polynomial multiplication with a quotient of x 3 and a remainder of 2?
To get a quotient and a remainder, you would need to do a division, not a multiplication.
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 ).
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
According to the Remainder theorem the remainder of the problem in which a polynomial F x is divided by the binomial x - a equals?
F(a)
When the polynomial in p(x) is divided by (x plus a)?
The result is a polynomial q(x) whose order is one fewer than the order of p(x) and a remainder term of the form b/(x + a).
What is a polynomial multiplication with a quotient of x 3 and a remainder of 2?
To get a quotient and a remainder, you would need to do a division, not a multiplication.
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 (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 ).
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.
If a polynomial is divided by (x-a) and the remainder equals zero then (x-a) is a factor of the polynomial?
false - apex
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
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
According to the Remainder theorem the remainder of the problem in which a polynomial F x is divided by the binomial x - a equals?
F(a)
What is divide x squared 3x-2byx-2?
To divide (x^2 + 3x - 2) by (x - 2), you can use polynomial long division or synthetic division. The result of dividing these two polynomials is (x + 5), with a remainder of 8.
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.
When the polynomial in p(x) is divided by (x plus a)?
The result is a polynomial q(x) whose order is one fewer than the order of p(x) and a remainder term of the form b/(x + a).
When a certain polynomial is divided by x - 3 its quotient is xsquared - 5x - 6 and its remainder is 5 What is the polynomial?
From the Division Algorithm for Polynomials theorem,f(x) = q(x)g(x) + r(x) or we say:dividend = (quotient)(divisor) + (remainder)In our case,quotient = x^2 - 5x - 6; divisor = x - 3; and remainder = 5.Substitute what you know into the formula, and you will have:f(x) = (x^2 - 5x - 6)(x - 3) + 5f(x) = x^3 - 5x^2 - 6x - 3x^2 + 15x + 18 + 5f(x) = x^3 - 5x^2 - 3x^2 - 6x + 15x + 18 + 5f(x) = x^3 - 8x^2 + 9x + 23 (this is the required polynomial)
